The Tigers were granted permission to speak to the 26-year-old after agreeing a £750,000 fee with The Rams for his services last month.
Hull are fully aware of the striker's capabilities after he finished the end of last season back at the KC Stadium after re-joining the club on loan.
Fagan, who has signed a three-year deal with the East Yorkshire outfit, becomes the club's first signing this summer in the process.
"Craig leaves with our best wishes and thanks for the hard work he put in at Derby," Rams boss Paul Jewell told the club's official website. "I don't think it's any secret that Craig wanted to make his deal permanent and I believe it's a deal that benefits all parties involved - both clubs and the player."