The west London club retain the option to make the switch for the 28-year-old permanent, while Stuttgart have also confirmed that Italian defender Cristian Molinaro has returned to his homeland to join Parma FC on a permanent deal.
Bobic: "Satisfactory solution"
"William hadn't quite been playing as regularly for us as he would have liked, and for that reason we wanted to find a solution that satisfied everyone," commented VfB sporting director Fredi Bobic. "We wish him every success there and hope he can get back to playing regularly again."
Kvist arrived at Stuttgart in the summer of 2011 from Danish powerhouse FC Kobenhavn and went on to make 68 appearances in the German top flight, providing two assists. He is also an established Denmark international, having scored twice in 44 appearances and represented his country at UEFA Euro 2012.
Molinaro joined the Swabians in January 2010 and went on to feature 93 times in the Bundesliga. The 30-year-old has also won two caps for the Italian national team.