"I'm very pleased to have got the deal done and I'm looking forward to contributing to this fantastic club," the 28-year-old told the club's website (www.fulhamfc.com) after joining from the Bundesliga club.
Kvist, who has played 44 times for his country, is a former team mate of Fulham's Norwegian centre-back Brede Hangeland having played with him for FC Copenhagen. He said Hangeland had convinced him top join Rene Meulensteen's squad as the Dutchman battles to keep Fulham in the Premier League.
"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," he said.
"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."
Fulham also brought in their former player Clint Dempsey from Seattle Sounders on loan this month, while Bryan Ruiz has left for PSV Eindhoven.
Other deals could yet be finalised before the window closes on Friday.
Fulham have lost their last three league matches and slipped into the relegation zone, just one place above bottom club Cardiff City, when they lost 2-0 at Swansea City on Tuesday.
(Reporting by Mike Collett, editing by Pritha Sarkar)
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