The 27-year-old says he is "surprised" but "very pleased" to return to the Championship side a month after being recalled by the Cottagers from his initial loan spell
The 27-year-old had already moved to the KC Stadium on loan this season in November, making five appearances for the Tigers before being recalled by his parent club a month later.
However, Fulham have now allowed Stockdale to return to Hull once again on a loan deal that will last until the summer, with the Englishman voicing his surprise at the move.
"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," he told reporters.
"I can't wait to get going again, and help the club to continue our push for promotion."
Stockdale has played three times for the Cottagers this season in the absence of first-choice stopper Mark Schwarzer.
The Australian has now returned to full fitness, though, prompting Fulham to allow Stockdale to return to the Championship side.
Meanwhile, reports have suggested that the Cottagers are looking to recruit Roma and Netherlands goalkeeper Martin Stekelenburg.