The 21-year-old ended his association with the Bavarian giants last month, completing a transfer to the 2.Bundesliga side and signing a contract until June 2019.
Green made his debut for Stuttgart in a friendly against MSV Duisburg on Sunday, and Wolf was encouraged with his display.
"Julian Green had a couple of good situations in his first game for us," Wolf told the club's official website. "It was clear to see that he has distinct qualities and that he can help us further."
After a half season with Bayern where Green made just two cup appearances, Wolf also acknowledged the young American international is lacking match sharpness.
"He certainly still needs some match practice, but he'll get that over the next few days and weeks," Wolf said.
Stuttgart returns from its winter break with a league match against St. Pauli on Jan. 29.