The 28-year-old has been at Stuttgart for two-and-a-half years after moving to the Bundesliga outfit from FC Copenhagen and will now form part of Rene Meulensteen's squad as the Dutchman looks to keep Fulham in the Barclays Premier League.
During his time at Copenhagen Kvist played alongside Fulham skipper Brede Hangeland and admitted his compatriot had him sold on a move to west London.
"I'm very pleased to have got the deal done and I'm looking forward to contributing to this fantastic Club," he told the club's official website.
"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 to be here 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."
Kvist has already been involved with training with his new team-mates at the Cottagers' Motspur Park training ground and is targeting an immediate place in the Fulham side that will host Southampton on Saturday.
"Of course I would like to be involved against Southampton but the head coach [Meulensteen] will see if I'm fit and able to play," added Kvist.
"I think I am, although I haven't played for Stuttgart this year, but I'm feeling fit and motivated.
"I just had my first training session and it was perfect. It was good to get to know the guys and talk to Rene Meulensteen about the tactical concepts and what his ideas are so I'm very much looking forward to my time here."
The terms of the deal give Fulham the option to make the move permanent in the summer.