The 22-year-old wideman moves to Elland Road initially on loan, but he has also signed a three–year contract with the club which will become effective from the summer.
The move brings to an end a three-year association with the Tigers which began with a loan move from Manchester United before a permanent deal was agreed in January 2011.
He made 55 appearances during an injury-disrupted spell at the KC Stadium, scoring twice.
Stewart spent much of the first half of this season on loan at Charlton Athletic and impressed with three goals in 18 appearances.