Darvich leaves Barca to return home to Germany, signing a deal to 2029.
The 18 year-old joined Barca as a 16 year-old from SC Freiburg and helped Germany win both the U17 Euros and U17 World Cup while with the Blaugrana.
Darvich said: "I am delighted that the move to VfB, such a special club, has gone through. I have also followed the Bundesliga regularly during my time at Barcelona and have been pleased to see the club's extraordinary progress.
"Now I want to settle in quickly, get to know my teammates and work hard to continue to develop and be successful in this shirt."
Fabian Wohlgemuth, member of the sports board at Stuttgart, commented: "We are very pleased to have signed Noah Darvich. He is one of the greatest talents of his generation and is already playing at a very high level.
"We also see significant potential in him, especially for his young age. We are convinced that he will have a very positive future with us."