Some further musings to consider.
There is good solid evidence that, for the first time in centuries, life expectancy is going down, not up. The reason is not disease, but lifestyle choices. Obesity, hardening of the arteries, risk-taking, violence, junk food, drug usage. The problem with lifestyle choices is that they are choices made by people, voluntarily. To reverse this trend, you need to get people on board. The problem is, how? Legislation? It worked for smoking and seat belts. Not so much for drugs. And your criteria seems to indicate it has to be world-wide. Maybe a world government that has teeth, and is willing to make the hard political decisions to force people into healthy life styles. Education sure doesn't work. So how do you universally enforce correct lifestyle choices in the entire population?
You are also up against a genetic barrier. It's not just telomeres that determines our life span. It is that cell reproduction is not perfect. It doesn not produce exact duplicates. The degradation of skin tissue, for instance, leading to wrinkles and dryness, is caused in part by the degradation of the cells through repeated replication. We don't have 'baby soft' skin at 80 because they are not the same cells - they have degraded in their DNA (or at least in their expressed DNA). It is possible to get creams and such to alleviate some of the damage (sun, for instance, and pollution), but to work on a global scale, people have to voluntarily use them. It is not a passive solution, it is active. People have to actively consciously decide to use them.
There are some genetic modifications that can increase longevity, but for these to become widespread in the population, it would take centuries, not decades. Unless, of course, there was a widespread policy of a genetic breeding program. For instance, if the population of the earth was reduced to just 1%, and this 1% was good genetic stock for longevity (the Japanese, for instance) there would be a dramatic increase in life expectancy for the survivors, but extending it to 250 years in the global population would take several generations of selective breeding. Maybe a world-wide plague that those who had longevity genes were immune to, by coincidence, and were the only survivors.
Some cancers are apparently caused by viral action, and cancer is the classic 'longevity' mechanism. If Cancer could be controlled, then cells would be made to reproduce indefinitely, just like cancerous cells do. In fact, it is posited that, for true longevity, cancer would not be cured, it would be made rampant, but controlled. Cancer research is the key to understanding the regeneration of tissue, and even stem cell activation. This, of course, is what cancer is - the uncontrolled reproduction of cells. But again, you have the issue of making this universal in all humans. A controlled cancer virus? Something that mutated? Doing this by genetic selection, again, would take umpteen generations, unless there were some mechanism for extinction of non-mutated humans. But a cancer virus, that caused a widespread controlled cancerous growth in all cells? The viral removal of or deactivation of the 'self-destruct' mechanism in cells that leads to the eventual death of the body, when they all decide to self-destruct without replication? (That, really, is what causes a natural death - cell death exceeds cell replacement, and there just aren't enough working cells to keep the body functioning).
Someone mentioned meditation. How about hibernation, where the entire metabolism, including cell reproduction, slows down? Say humans hibernated (suspended animation?) for four months out of twelve. Would this extend our life expectancy by the same ratio? Again, this could perhaps be done using drugs (that choices thing) or a long-term genetic modification approach (Inserting hibernation genes into the human genome) but is living to a calendar age of 250 the same thing, if you aren't conscious for one third of it? We live longer, but we don't get any experiential benefit from it. Of course, we would live long enough to see our great-great-great-great-great grand children, and would witness the advances of technology and of civilization. But living to be 250 just to say we lived to 250? What about quality of life? Would we choose to? That life-style thing - how to make it passively universal.
You could, of course, pull a Stephen King, and just assume longevity, without explanation. Stephen King did some really weird unexplained and unexplainable things in his novels, but really didn't do it in a fantasy or sci-fi way. He just wrote his novels based on considering them as part of normal, every-day experience, and didn't worry about science. It would not be beyond such an author to posit that, two universes had become super-imposed, one with a value of the constant c that we are familiar with, and another with a drastically reduced value for c, and humans living in each one, side by each. Relativistically, through time dilation, the high-cee group would apparently experience time going by much slower than the low-cee group. That is, one group would see the other group moving in very slow motion, and the other group would see the first group moving extremely quickly. Comparatively, one group would live for 250 years, and the other for 150 years, in the same relative life span. It would be like one group had left on a generation ship for 250 years, and then came back to earth. People on earth would experience 250 years gone by, but people on the ship would experience only, say 150 years. This would be stretching and bending things, but not really violating any laws or theories that have not been proposed by string theory and such. Stephen King would be proud.
An extension of this, is to somehow speed up the earth. Time would go slower. (Incidentally, the reverse is happening - since the earth is slowing down, time is going faster on earth today than it was when the earth was first formed). How this could happen would be another Stephen King - you just assume it happened, with no explanation. The mysteries of physics. If they want us to believe in black holes, why not this? (Basically, that is Stephen's answer). The emphasis is on the human reaction, not the science. What reader takes the time to question the science in a Stephen King novel - they are too busy being either scarred or shocked or otherwise engaged in the story?
But this brings up another unresolved issue. Consciousness. Within the last ten years or so, credible scientists with excellent credentials (Nobel prizes) are seriously positing that consciousness is a result of quantum phenomena. We know that life itself makes extensive use of quantum techniques. Things that biologists could never understand, are explained by quantum tunneling (ion transfer across membranes, photosynthesis, birds detecting magnetic fields, for example). Quantum theories have done more to explain day-to-day mysteries here on earth than Einstein's theories ever did. So, something that has never been tested - what does time mean to quantum biological events? Planck had a very different idea of time than did Einstein.
We know that live plants and humans sent into space are not as 'old' as their equivalents on earth, when they come back, but what is the conscious experience of the organism during this time? What is their biological experiential age when they come back? Does the astronaut really feel any younger than he would have if he stayed on earth? Do they grow as if they are still on earth, in the same time frame? Time is not the same concept for conscious experience as it is for physical phenomena. We talk about 'that day went fast' or 'this month is really dragging', as if the passage of time is variable, relative to something else besides physical reality, the 'clock'. That is why there is a definite movement to consider quantum time as something different than relativistic time. In quantum physics, nothing is defined until it is consciously experienced. Is it the same with time? That time has to be consciously experiences to have any definition?
What would conscious time be like for a human that lives to 250? How would they experience the passage of time? How would a human on a generation ship experience the passage of time? Would their quantum consciousness be so connected to their earth foundations (entangled, as it were) that they experience that they really were traveling for 250 years?
We know physical time is relative, but what about biological conscious time? Call it biological quantum consciousness time. Is that relative and if so, to what?
How would humans experience life and the passage of time if they lived to be 250? How does a bowhead wale experience its 200 year life span? If they can live to be 200, there is no real biological impediment to a human living to be 250.
These issues and ideas are all fair game for a novelist to explore, when dealing with positing a life span of 250 years for a human. Is the issue all about science, or is it about character development and social repercussions, human issues?