Burke came through the academy at West Ham but made just 15 appearances in the first team, spending loan spells at three different clubs.
During the last campaign, the 21-year-old spent two separate periods at Bolton Wanderers, where he featured on 25 occasions in the Championship, and the young Englishman has now opted to pen a three-year deal at fellow second-tier outfit Hull.
Burke told the club's official website: "I'm over the moon to have signed for Hull City. I enjoy playing football and I see this move as a big opportunity for me.
"I've had a good chat with the head coach and I know that the club were really keen to bring me here. That is a nice feeling to have."