I wanted to give some time for answers to percolate before providing any answer of my own, but I'd make a few observations, to ground the analysis, without really resolving some of the trickiest and most interesting parts of the question.
Lots of a military force involves an Air Force and a Navy in addition to the Army. In 2015 in the U.S. military, the force structure was:
- Army 491,177
- Navy 326,504
- Air Force 312,195
- Marine Corps 184,587
- Coast Guard 40,069
In the Air Force, very few personnel actually enter the "battlefield" on a plane, about 95% of the personnel supporting each aircraft are ground crews, where issues of physical strength could be addressed with greater use of machines for lifting and applying strength.
The number of pilots in the Air Force is sufficiently small that your recruits can be very gender atypical, e.g. in emotional and personality character, and still easily to secure in sufficient numbers.
Physical strength and size aren't particularly important in pilots, and the crew portions could be adapted in size for women fairly easily.
The Air Force is currently 19.1% female.
A meaningful subset of the Marines are part of its own internal Air Force to which similar considerations would apply.
Navy and Coast Guard
Many positions in the Navy call for sailors who are actually below average relative to men generally in size, especially submarines. And, relatively few positions on a modern ship call for exceptional physical strength that could not be replaced by more intense use of machines to assist in lifting and moving things. If anything, an all female ship or submarine might more easily achieve a cohesive crew on a long deployment than a ship with only men.
Most of the hand to hand combat training in the Navy is directed at sailors maintain order vis-a-vis other crew members who get unruly, and protecting ships that are docked when it is not necessary to carry lots of heavy gear over long distances on foot.
The U.S. Navy is currently 18.1% female, the U.S. Coast Guard is currently 14.8% female.
While some specialties in the Army fit the traditional stereotypes of what a soldier is, many do not. The U.S. Army is currently 14.2% female.
Lots of soldiers in the Army and lots of Marines (which is currently 7.7% female) have jobs like driving supply trucks, providing medical care, maintaining equipment within forward operating bases, feeding the troops, reviewing intelligence from drones and satellites and troops in the field, and so on. In military lingo they are called "Fobbits" because they work in "forward operating bases".
Certainly resources like artillery have become more accurate and have required less crew support over time, requiring fewer personnel to achieve the same military outcomes.
Another role that was traditionally in the front lines and considered to require physical traits associated with men was operating a tank, even though there were maximum personnel size limitations on tanks. But, the number of tanks in the active duty force has declined greatly, because they have become less militarily useful in modern conflicts, and the tanks that remain have become more automated. Many proposals to make tanks even more automated have been rejected because they weren't a priority, but could be adopted in an all female force.
New positions like drone operators also don't have very gendered demands on personnel. Neither do some quite front line positions like helicopter operators.
Certainly, positions like infantry and special forces would be very strongly impacted, and how those posts in the military would change is very notable. But, those positions are a minority of the modern military, and the changes would be far less dramatic than they were in the days when infantry fought with swords rather than firearms.
If one assumes that the Air Force, the Navy, the Coast Guard, and the aircraft operating part of the Marines won't be much different, those components of the military, which make up about half of the U.S. military personnel, wouldn't change very much in character or capabilities.
The Army and Marines would certainly be impacted more, but probably only about 1 in 3 members of those forces would be in the kinds of positions that would be impacted very much. Perhaps up to 250,000 personnel out of almost 1,355,000, or about 18% of the force would have strongly impacted by the transition in how they could or would operate.
Thus, about 82% of the force wouldn't change very much, while about 18% of the force would change a lot in some of the ways discussed in other answers. How that 18% would change is very interesting, but one shouldn't overstate how representative that portion of the force is to the entire military force either.
Transition Period Duration
There would have to be a transition period during which men were phased out of the military and women were phased in, because lots of military skills can only be learned by doing under the supervision of people who know those skills.
But, this wouldn't take terribly long because the military is constantly cycling through personnel. Much of the active duty force serves for four to eight years before returning to civilian life, ten years would be longer than average, and twenty years is about as long as a military career gets.
So, over twelve to sixteen years, a very large part of the transition could be completely relatively seamlessly, without catastrophic loss of skill sets limited to experienced veterans. If there were a greater rush, an eight to ten year transition could still be manageable although it would carry higher costs particularly in the loss of skills at higher ranks where personnel turnover is not as rapid.