The ninth Doctor claimed he'd been travelling in the TARDIS for 900 years in The Empty Child. It's generally accepted that he actually left Gallifrey late in life, so my personal theory based on all the dates previously given is that he's about 1300 years old but has in recent years begun counting his age from the time he started travelling, discounting the time before that. Otherwise, it makes little sense as he seems to be aging backwards. As I recall, Steven Moffat has said that RTD was perfectly well aware that the 900 years thing was wrong, but felt that it was a number more likely to be accepted by the new audience than if he'd said 'over a thousand'.
For the record: the second Doctor said he was 450 in Tomb of the Cybermen, and the next clear date we're given (barring a few comments from Jon Pertwee so vague that they could mean anything) is when the fourth Doctor claims to be a little over 750 (much time having evidently elapsed between televised adventures). The sixth Doctor is around 900 when he first appears, and by the time the seventh turns up he's 953 (Time & the Rani). The Doctor later celebrates his 1000th birthday in one of the novels published in the nineties, and the eighth subsequently spends a hundred years stranded on Earth. If you count these, he has to be at least 1100, if not he still has to be well over 950. It was suggested in one of the books that the first Doctor had been travelling for 60 years before the first televised story, and there's obviously little time passed between his first incarnation and Tomb of the Cybermen (he has human companions throughout that period) so he must have been around 390 when he left Gallifrey. Add the ninth Doctor's '900 years of phone box travel' and you get a figure of about 1290.