The 28-year-old had been linked with numerous clubs including West Ham and French Ligue 1 outfit Evian, but Fulham have won the race for his signature.
The Cottagers also have the option to make the transfer permanent at the end of the season for a fee which is understood to be £1.2million.
Kvist is an established member of the Denmark squad, with 44 caps for his country, but he had fallen out of favour at Stuttgart.
He has been with Stuttgart for two-and-a-half years after moving to the Bundesliga outfit from FC Copenhagen where he was a team-mate of Fulham defender Brede Hangeland.
Kvist, who could make his debut against Southampton on Saturday, told Fulham's official website: "I'm very pleased to have got the deal done and I'm looking forward to contributing to this fantastic club.
"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.
"When I was a child I used to just watch English football on television so it's amazing being here.
"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.
"Of course I would like to be involved against Southampton but the head coach 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."