He said the book, which concentrates on the end of Henry VIII's marriage to Anne Boleyn, had made "one of the best-known pieces of English history" come alive again "as though for the first time".
The judges, who included Downton Abbey star Dan Stevens, spent just over two hours making their decision in what Sir Peter described as a "rigorous process of literary criticism".
Mantel received a cheque for £50,000 at the event at Guildhall after seeing off competition from five other contenders including journalist and novelist Will Self's book Umbrella which had been among the favourites to win.
When she accepted her prize Mantel said she felt "lucky and privileged".
She said she now faced the "very difficult" job of writing the final book in the trilogy. She said: "I assure you I have no expectations I will be standing here again".