Stockdale, 27, spent a month on loan with the Tigers prior to the Christmas period, making five appearances, before starting three games for Fulham at the turn of the year, but was back in Hull's colours in their weekend draw at Peterborough.
"I really wanted to be a part of this until the end of the season because it's such an exciting time," Stockdale told Hull's official website.
"The (Fulham) manager asked me if there was anywhere in particular I wanted to go and I made it clear I wanted to come back to Hull.
"There's a fantastic group of lads here and the team also plays great football."
- Sports & Recreation