The player was believed to be close to joining the Cottagers after Stuttgart head coach Thomas Schneider revealed that he was looking to leave, but Fulham have now confirmed the deal on their official website.
Fulham also announced that there is an option in the deal to make the transfer permanent at the end of the season, for a fee undisclosed but believed to be £1.25m.
"The club is delighted to confirm the signing of William Kvist on loan until the end of the season," a statement read. "Kvist arrives from German outfit Stuttgart, and Fulham have an option to make the transfer permanent in the summer."
"I'm very pleased to have got the deal done and I'm looking forward to contributing to this fantastic Club," Kvist told the club's website. "Of course I've heard a lot of good things from Brede Hangeland and it's been a target of mine to come here so I'm delighted to be here really.
"Of course I would like to be involved against Southampton but the head coach [Rene Meulensteen] will see if I'm fit and able to play - I think I am, although I haven't played for Stuttgart this year, but I'm feeling fit and motivated."
Kvist has been capped 40 times for Denmark, but did not play regularly for Stuttgart this season.