He says in "The Day of the Doctor" he is 1200 (but he doesn't know if he is lying) and the time skips are about: 1. 300 2. 500 so the Doctor is about 2000 give or take
After the events and time that took place in "The Time of the Doctor", Peter Capaldi in "Deep Breath" is quoted as saying "I'm the Doctor. I've lived for over 2000 years..." This took place in the same couple of days (relatively speaking) as the regeneration from Matt Smith to Peter Capaldi.