Last weekend's 2-1 defeat to Wolfsburg may have been their 17th in the league this season but, with the three sides below them all losing, Stuttgart's safety was confirmed and they can now plan for next term.
Defender Klein, 27, has made 23 league appearances for Austrian champions Salzburg this season and was also part of their UEFA Europa League campaign that saw them reach the last 16.
Klein moved to Salzburg in 2012 but has chosen to move to Germany rather than renew his contract in Austria.
Stuttgart have agreed a three-year contract with the Austria international and Fredi Bobic believes that he will help them improve after a season fighting against relegation.
"Florian is a very seasoned player with more than 200 games in the Austrian Bundesliga," said the sporting director.
"He also brings international experience from games in the Europa League and the national team of Austria.
"We are convinced that he will be quickly integrated with us and strengthen our right side."
