The 19-year-old Manchester United forward has extended his stay at the KC Stadium until the end of the season and has so far started eight games.
He told the club's official website: "I've been pleased with my performances, although I'm just pleased to be starting games and playing regularly.
"To be here for six months is going to be good for me, a chance to get regular games and grow up in the game."
Stewart's contract at Old Trafford expires in the summer and he may have to consider his future options.
However, he is fully focused on making progress at Hull and added: "We've been on a good run in the league recently and hopefully we can carry that on and maybe make the play-offs."