We don't know how old the Doctor was when he first regenerated(in "The Tenth Planet"). However, in "The Tomb of the Cybermen" the Second Doctor said that he was "something like 400, 450 years old". In the later story "The Brotherhood" (comic story), the Second Doctor stated that he was 500 years old. And promotional material for "Spearhead from Space" said that the debuting Third Doctor was 500 years old.

In real-life, the actor Patrick Troughton was 46 years old when he first appeared as the Doctor(at the end of "The Tenth Planet"), and 49 years old at the end of "The War Games".