The 21-year-old, who spent the first half of the season on loan at League One outfit Carlisle, has signed a three-and-half-year contract.
Chester told Tigers Player: "I'm really excited. It's all happened quite quickly. As soon as I heard about Hull's interest it excited me.
"It's the next step up from where I've been. To come to Hull is another challenge and something I'm looking forward to.
"Hopefully I'll play as many games as possible, but I need to prove myself first."
Chester will be unavailable for the weekend FA Cup tie with Wigan having already played in the competition for Carlisle, where he scored four goals in 24 appearances.