Veh announced in March that he would step down as Eintracht Frankfurt coach at the end of this season, a revelation that led to speculation over his next destination.
However, it was revealed on Monday that the 53-year-old would be heading back to the Mercedes-Benz Arena to replace the departing Huub Stevens.
Veh was previously at the helm between 2006 and 2008, guiding Stuttgart to the Bundesliga title in his first full season in charge.
And the 53-year-old is determined to write another successful chapter in the club's history.
"We have very good discussions, and I have great joy and pleasure in mind here to build something again in Stuttgart," said Veh. "I have very fond memories of the club, the people and the environment I know here.
"VfB has great potential and I am convinced that we can club together to advance properly."
Chairman of the supervisory board Dr Joachim Schmidt added: "Armin is an absolute professional, he brings a lot of experience, knows the club and fits very well for VfB."
Veh guided Frankfurt to a 13th-place finish in the Bundesliga this season.
