The goalkeeper initially moved on loan to the KC Stadium in November and made five appearances for the Tigers.
He was recalled by Fulham in December when first-choice goalkeeper Mark Schwarzer suffered an injury.
Stockdale played three times for the Cottagers in Schwarzer's absence, but the Australian has now returned to full fitness and has reclaimed his place in goal.
"It came as a bit of a surprise to everybody here when I was recalled a few weeks ago, but I'm very pleased to be back," Stockdale said.
"I can't wait to get going again, and help the club to continue our push for promotion."