That is question... and one that has been debated for over 400 years. And one we probably never have the answer to. Right now, the two bodies thought to be the princes (discovered in the reign of Charles II) have not been subject to any modern forensic testing (the last examination was in the 30's before carbon dating, dna testing, forensic reconstruction, etc.)

The Tudors did there best to blacken his reputation to make their claim of the throne more forceful.

An overview of the case can be found here:
http://www.crimelibrary.com/notorious_murders/famous/the_princes/1.html