Boyd, who saw a transfer deadline day move to Nottingham Forest controversially break down last month due to an inconclusive eye test, has signed for the Tigers with a view to a permanent deal in the summer.
His move will be for an eventual seven-figure sum, according to Peterborough's website.
In a statement on www.theposh.com, the 27-year-old said: "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.
"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 helped Posh to three promotions during his stay at London Road and scored 75 times in his six years at the club.