Posh chairman Darragh MacAnthony had previously turned down numerous bids from the Tigers for the attacker, who joined the Cambridgeshire-based outfit from Stevenage Borough in 2007.
However, the 27-year-old has admitted that he requested a switch to the KC Stadium to provide him with a better chance of playing in the Premier League.
"I would like to especially thank the chairman Darragh MacAnthony. The chairman and I spoke at length and he informed me he had turned down five bids from Hull City and three other bids from three other Championship sides because it was not about the money. He was desperate to keep me at the football club so that Peterborough United had a better chance of retaining their Championship status," he told the club's official website.
"However, I explained that the opportunity to join a club like Hull City at this stage of my career was too good to turn down. I didn't want to wait until the end of the season. I wanted to fulfil my dream of playing in the Premier League.
"The chairman told me of his desire to back the manager as much as he could in every attempt to keep Posh in the Championship, which I fully understand and after a long and emotional telephone conversation, he and the manager, reluctantly agreed to let me go and try and fulfil my dream."
Boyd has joined Hull initially on loan, with the deal to be made permanent during the summer.