Monchengladbach confirmed the signing of the Guinea international on Monday, with the former Hertha Berlin and Augsburg man to be under contract at Borussia Park until 2018.
Traore has been a regular for Stuttgart in the top flight since arriving in 2011, with sixth-placed Monchengladbach looking to bolster their options ahead of a potential European campaign next term.
Augsburg's Andre Hahn has already agreed a close-season switch to Borussia Park, and Monchengladach's sporting director Max Eberl stated Traore's versatility made him an ideal signing.
"Ibrahima Traore is an extremely fast winger with whom we are more flexible in attack," he told the club's official website.
"He is a free transfer and we are delighted that he has opted for Borussia."
Traore played the full 90 minutes for Stuttgart against his future employers on Saturday as Monchengladbach secured a dramatic 1-1 draw thanks to Juan Arango's 89th-minute equaliser.
