This is slightly long, my apologies for that. I've tried to go into a little bit of detail so that my answer can be of some real use if you ever choose to actually write such a scenario.
There are already some good answers up here. Most of the answers, however, seem to involve drugging the wizard and/or suicide. I see some logical problems there. Now the idea as a whole makes sense, don't get me wrong. But it leaves a few variables in the air.
The Problem with your Problem
The Question states that the secret union of Kings has already decided. The order is issued. And the method is already decided too.
The soldiers are going to turn on their generals, kill him and the highest position takes command a'la Order 66 as DJMethaneMan rightly pointed out. Here's my problem with it:
Order 66 was in a sci-fi world where every single soldier had a handsfree communicator in his helmet. If you have that level of tech, well this problem is easier to solve. But from your question it doesn't appear to be the case.
How will you tell every single soldier this is what the plan is? More importantly, how will you make sure some loyalists won't tell on you? You see, in the Order 66 scenario of Star Wars, it happened to quickly that even if someone wanted to warn the Jedi, they wouldn't have had enough time. It was an instant communication, executed immediately.
In your question, if someone wanted to tell a regiment of soldiers they were supposed to turn on their general, it'd have to happen in an announcement (which the general might overhear), or a code, or secret letter or some such. The sheer amount of time needed to make sure everyone knew this was to be done would give some people the time to tattle. And then poof. Teleportation.
So you got a problem.
In Re Sedation or "whacking on the head"
Whacking someone on the head with the exact amount of force needed to knock him unconscious but not enough to kill him? While making sure he doesn't see it coming? Do you know how easily a head injury turns into instant death? Sounds more like Tall Order "X".
Drugging. Now that's more like it. Sedate the buggers. You would have to consider one thing though - the Wizards aren't gullible idiots (unless that's how you wanna write them). A being of such immense power is probably aware that there must be a contingency plan in place in case he turns rogue. Even if he doesn't know there's a secret meeting taking place in some hidden bunker, he will have social interactions with other wizards. Imagine how that interaction goes.
"Hey Phil, how's the wizarding?"
"Not bad Joe. Say, where's Eric, John, Nathan and the rest?"
"Don't know, they've been missing. It's odd now that you point it out. But I'm not really thinking about it."
"Oh well, nevermind then. By the way how delicious is this soup? It's making me dizzy."
Firstly, if I had this power set, I'd know sedating and remotely/suicide killing me is the quickest and safest way to get to me. I'd be wary. You can't just hand me a bowl of soup and expect me to wolf it down without being suspicious every single time. If I'm a general, I'm pretty much trying to make sure that the enemy isn't doing exactly what you're proposing to do. Therefore, my guard is already up against this tactic in any event.
Secondly, this mind-transfer spell is like an auto-activate situation. The wizard isn't doing anything here, the spell is. More on that later.
Thirdly, if I were a wizard and I found out wizards have been going missing, I'd teleport instantly to a hiding place. I'd appear once my magic is recharged to a place full of civilians to facilitate quick mind transference, go into hiding and not reappear for however long it took for Order X to die down. Or worse, I'd meet up with other wizards, designate a date and time for simultaneous assassinations. Selected wizards (who draw the short straw) would teleport to the Kings involved with a loaded crossbow when they're asleep. It might be suicidal, but clearly, both sides are capable of that.
A summary of the Issues
Now, why have I labored on potential problems for so long? Because I have potential solutions. Allow me to summarize the problems:
A wizard can blink away without warning or preparation. Gotta catch him by surprise, or use his subsequent powerlessness as an advantage.
He can mind transfer, and he need not even know he's about to die. Death just needs to be imminent for the spell to auto-activate.
He's not a buffoon. Wizards are also capable of making plans and taking revenge. So it needs to be quick and simultaneous, and not painfully predictable.
The killer might be facing down a hydra or dragon or whatever mythical creature you're referring to. Or stuck banging his sword against an impenetrable force field.
Is it even possible while avoiding suicide?
Enter the Counter-Magi Division (or the CM Division)
Imagine a secretly maintained force of assassins, specializing in hunting and killing wizards. Any one of these men or women could take on Jason Bourne and eat him for breakfast. They are in peak physical condition, trained in every known way to kill, equipped with cutting edge technology and have studied wizards all their lives. They move like shadows and would give Rikimaru a run for his money (basically they're stealthy as hell).
They are planted at random positions in a Wizard's regiment, obeying him as their general and gaining his trust until the time to strike comes. How would they kill the wizard, while minimizing risk of suicide and/or revenge upon their Kings?
Let's play with a few ideas.
The Issuance of Order "X"
Upon issuance of Order X, the relevant operatives of the Counter-Magi Division are all conveyed their specific orders. They are planted in the relevant regiments and given a specific date and a two hour time range to complete their missions.
A few months pass. Each Wizard has had eight to nine operatives secretly working under him for a while now. At least one or two of them have his trust. The night of the execution arrives. The operatives spread out over a 1 km radius, dividing the areas equally.
The entire garrison is then poisoned. How? Odorless gas, spread through ventilation systems or just releasing it upwind if the camp is on open ground. The poison is a new type, recently developed in the CM Division labs and has a simple liquid antedote that can be consumed with water. Cutting edge technology remember? The poison is slow acting and does not take effect till a few hours later.
One operative goes to a designated safehouse. One operative stays back and arranges a fake assassination attempt on the wizard. The rest as spread out as mentioned above. Please note that the operative who stays back is not trying to kill the wizard himself, but rather the Covenant of Thrones (or whatever your Kings united are called) has hired idiot assassins for an attempt on the Wizard's life. This is important: the fake attempt must be by numerous assassins making physical escape look almost impossible. The idea is to corner our guy into teleporting.
The Operative comes to the rescue of the wizard, telling him that there is a safehouse closeby, within teleportation range. This is the guy the wizard hopefully trusts. This can play out in various ways:
The Wizard says "Ok thanks!" and teleports as per directions. Upon his teleportation, the operative releases a yellow flare. The wizard teleports to find one of the hidden operatives waiting to slit his throat. The operative does the deed and shoots a blue flare into the night sky. Good night. Job done.
The Wizard says "Ok thanks!" and teleports to a location of his own choosing. The operative who told him to teleport releases a yellow flare. The operative waiting at the safehouse waits a short while then shoots a red flare into the night sky. The other operatives go on the hunt. They have 24 hours to get this guy. The Operative who stayed back to deceive the Wizard then conveys the orders to the rest of the regiment - no more fear of the men tattling. Also, he gives them an antidote for the poisoned gas. The soldiers start a manhunt, led by the specialized operatives. Remember, the Counter-Magi Division operatives are experts, they know what they're doing and they've trained all their lives for this hunt. So chances are they'll find their guy, who happens to be powerless, exhausted and scared shitless. I think they'd find him in 6-7 hours. If they don't? Eight hours passe since his escape. The slow acting poison kicks in. The spell does not activate so he dies. Done.
He says "Fuck you I knew you're betraying me!" and kills our Operative. He rallies the soldiers and slays the assassins. Damn. That went sideways. He doesn't teleport because he knows his auto-activate power is an irreplaceable fallback. Now even if the poison kicks in he'll just be switched to another body. He simply goes on the run in a conventional manner. Since no yellow flare was released, the operatives converge on the center of the 1 km radius from all directions. Chances are they'll find him, because hey, Jason Bourne for breakfast, trained all their lives etc etc. But what do you do once you find him? Put him through incredible torture until he's forced to teleport. Cut off one finger at a time, give him the chance to teleport to save himself. Careful now, don't want him dying on you. Hurt him without killing him, until he's forced to teleport. He might summon a hydra or something but our operatives can handle that stuff because the Jason Bourne thing dammit. Finally the bugger teleports, and deal done. He won't walk away from this poison. Save some antidote for the garrison.
He says "Fuck you I knew you're betraying me!" and kills our Operative. He rallies the soldiers and slays the assassins. Damn. That went sideways too. He doesn't teleport because he knows his auto-activate power is an irreplaceable fallback. Now even if the poison kicks in he'll just be switched to another body. He simply stays at the garrison and asks the soldiers to protect him with their lives. They don't know about Order X yet, so they do what he says. Big mistake. Again, no yellow flare is released so the operatives converge on the garrisson and send one man to yell at the gates. The operative literally just holds up the royal decree confirming Order X and tells the soldiers to get the wizard. Remember he still doesn't know he's poisoned. He could kill himself and just do a mind transfer but it wouldn't make sense. Why give up half your life if you can simply escape with all of it? So he teleports. The operatives ascertain that he's escaped and release the blue flare. Post teleportation his auto activate won't save him. Mission accomplished.
The same premise as number 4. When the operative arrives to yell at the gates, the wizard decides to kill himself and do a mind transfer rather than teleporting. The operatives leave the 1 km radius immediately (after testing each other on basic identity confirmation questions) and take the antidote. The garrison/city dies with the wizard in it. High cost, I know, but it is an unlikely scenario. I frankly don't see it taking place.
For some reason, the city/garrison decides to stick with the wizard and protect him. Ditto as 5. Bad outcome, but highly unlikely, and still gets the job done.
In summary, you don't trigger the mind-transfer at all. Force his hand to teleportation and ensure a clever and unforeseen delivery of the poison. Some wizards might still get away, life is full of unpredictable variables. But I reckon the CM Division would deal with 99% of your problems in one bloody and brutal night. The 1% could still be dangerous, I realize that. Keep your Kings and important officials in hidden locations for some time and let the CM Division wrap things up.
They know what they're doing.
BONUS FOOD FOR THOUGHT - How well thought out, and well conveyed is your magic?
At no point in a story do you want your readers to go, that made no sense. If you have powers like mind transference, you should consider placing a mildly explained at mechanism at play. This is generally a rewarding rule for all magic. Look up Sanderson's Laws on Magic for some interesting reading on the subject.
In light of the above, some thoughts on mind-transference.
The spell can, to a certain degree, predict that the wizard is about to die, so it activates and transfers his mind. The phrasing of the question seems clear enough - the spell realises that death is imminent and does the transfer, not the wizard. I'm going to draw the most logical conclusion from this phrasing to state:
The wizard doesn't need to know he's dying. Just the spell or the magic that resides in him does. The wizard doesn't even need to be awake. I could be knocked out but the spell would still complete the transfer automatically.
"If death is imminent" basically means if death is likely to happen in the future. How does the spell know that death is imminent? Premonition based on facts available?
My understanding is that the spell can predict possible futures based on what it knows. If death is the most likely scenario, the spell will activate.
So if the wizard is fighting someone and the assailant gets close enough to cut his head off, the moment the blade touches the skin of the wizard's neck the spell will go into prediction mode and see if the wound is lethal. If the wizard might die, boom, mind transfer, new body acquired before the decapitation is even halfway through.
How far ahead into the future can this spell see? How much can the spell discriminate between situations of danger? Is the spell informed by just facts or also the thoughts and knowledge of the wizard?
The Omniscient Immortality Formula: Let's take one extreme interpretation of the above just to see how it plays out. If the sub-conscious of the wizard is aware that someone may sedate him as a common method of killing him (as explained above), will the spell know that sedation means death even if the sedating agent itself isn't going to cause it? The spell would then immediately cause a mind transfer. Game over. The wizard is practially unkillable then.
By its very nature, the question acknowledges that death is possible. So I will assume that the spell can be fooled to an extent. Let's set limitations for this power before we proceed. I don't want to nerf it too much, but I don't want to make it imba (too strong) either.
The spell can only know when the imminence of the death is pretty much physical. The spell is not sentient, it doesn't connect to the wizard's brain or thoughts. It surveys physical symptoms and reacts. If the body is dying, it activates. It will not activate if death is likely or even a certainty until the body evidences so.
So the beheading example from above can remain intact while still excluding the omniscient immortality formula that I mentioned after that. It will make for interesting reading without making the wizard's death/survival obvious and predictable IMO.