The 21-year-old forward joined the Reds from Leeds United for a reported £1million in the summer.
He played 16 games, eight from the start, and scored against Luton Town in August but his last match was the 4-2 home loss to Stoke City on November 9. He has not featured at all under current head coach Gerhard Struber.
Wilks will now link up with Hull boss Grant McCann who was his manager at Doncaster Rovers last season.
He is the latest out-of-favour player to leave Oakwell during the January transfer window following the departures of Cameron McGeehan to Portsmouth and Jordan Green to Newport County.
Struber is also understood to be willing to let defenders Dimitri Cavare, Dani Pinillos and Toby Sibbick leave as well as winger Mamadou Thiam.
