The Denmark midfielder will spend the remainder of the Premier League campaign at Craven Cottage.
Fulham then have the opportunity to secure the services of Kvist for the long term when his loan runs out.
A former team-mate of Fulham's Brede Hangeland at FC Copenhagen, Kvist joined Stuttgart in 2011.
He told his new club's official website: "I'm very pleased to have got the deal done and I'm looking forward to contributing.
"Of course I've heard a lot of good things from Brede and it's been a target of mine to come here, so I'm delighted really.
"The Premier League is the biggest league in the world. I’ve played in the Bundesliga, which is also a really nice league, but this is the biggest challenge you could get as a footballer – this is the motherland of football.
"When I was a child I used to just watch English football on television so it’s amazing being here."
Kvist could make his debut for Rene Meulensteen's men on Saturday when they host Southampton.
