The 47-year-old takes the place of Huub Stevens, who leaves the club having saved them from relegation for a second year running.
'Looking forward to this challenge'
"We're pleased to have appointed Alexander Zorniger as our new head coach," said Stuttgart's sporting director Robin Dutt. "We have a concept for the club in mind and Alexander Zorniger's ideas of how football should be played are very similar. It's about finding our way back to the VfB school; to our own identity."
Zorniger is no stranger to Stuttgart, having worked as assistant to Markus Babbel in 2009. "I'm really looking forward to this challenge at Stuttgart and I'm convinced we can build something here together," he said. "It's something special to be head coach of this club, in my own home region."
Zorniger previously worked at SG Sonnenhof Großasbach, leading them to promotion to the third division in 2012. He then guided RB Leipzig from the fourth into the second division before parting ways with the Saxon club by mutual consent back in February. He takes charge of a Stuttgart side who avoided relegation in the final 20 minutes of the 2014/15 Bundesliga season thanks to a 2-1 win at SC Paderborn 07.