Dumbledore was approximately 150 years old when he died, according to J.K. Rowling.

Question: How old is old in the wizarding world, and how old are Professors Dumbledore and McGonagall?

J.K. Rowling: Dumbledore is a hundred and fifty, and Professor McGonagall is a sprightly seventy. Wizards have a much longer life expectancy than Muggles. (Harry hasn't found out about that yet.)

Scholastic Chat - 10.16.00

I'll add this from the Harry Potter Lexicon, which addresses the fact that Dumbledore's age seems to be less than 150 at the time of his death:

Birthdate: 1881 (JKR), probably in July or August. This date supercedes Jo's statement in 2001 that Dumbledore was "about 150 years old" (Blue Nose Day) and fits better with the dates that appear in Book 7. Regarding his month of birth, Rita [Skeeter] says that Dumbledore was “nearing” his 18th birthday when he left Hogwarts in June, but was still 17 when he met Grindelwald (DH18). Basically, at some point during Grindelwald’s stay at Godric’s Hollow Dumbledore turned 18, so the month of his birth appears to be July or August.

Harry Potter Lexicon - Albus Dumbledore

Basically, it boils down to JKR is really really terrible at her math!