As I'm sure you've noticed Hollywood's latest crop of upcoming poorly thought out films includes "In Time", a film where people no longer age but to prevent overpopulation they are only allowed to live so long and use their remaining time as currency. There are so many ways that could not work.
For one thing, that system would require a lot of new births to prevent deflation as time is depleted, kind of contradictory to the intended purpose. But that's beside the point, there are far less controversial ways to regulate immortal populations.
The simplest one would be to surgically sterilize anyone who becomes immortal. Considering how radical such a procedure would be it should be trivial to add in a vasectomy or tubal ligation. That simple act would discourage many groups from becoming ageless in the first place, unfortunately those same people are the same ones largely responsible for the planet's high population growth in recent decades. Still, the lure of eternal youth is sure to snare a majority of the populace over the centuries.
And if you're concerned about a slow extinction from attrition as no one has kids, don't be. If there's room for more people the government can allow some people to reproduce using stored sperm and ova or as a last resort, cloning.
Still, those measures are most likely not enough, fortunately the technologies to construct habitats in space or the ocean seem to be more feasible than completely halting aging. Thus making more room for our growing population before we have to deal with such a crisis. Though somewhat limited life-extension is probably more doable than transporting a significant proportion of the population out of earth's gravity well.