The 27-year-old Austrian international, who can also play in midfield, will join on a free transfer in the summer on a deal set to run until July 2017.
'One of the best'
"Florian is a very experienced player with more than 200 games under his belt in the Austrian Bundesliga," said VfB sporting director Fredi Bobic. "He also brings international experience both in the [UEFA] Europa League and with the Austrian national team of Austria. We are convinced he can be quickly integrated and he will strengthen our side."
Stuttgart secured their Bundesliga status for another year last weekend, despite losing at home to VfL Wolfsburg, and Klein cannot wait to get started at his new club. "The German Bundesliga is one of the best leagues in the world," he said. "I am glad that I can represent such a historic club like Stuttgart next season."