The midfielder, 18, has yet to feature in a first-team league match, but made 24 appearances in the Under-19 Bundesliga for Gladbach last season.MORE: Alex Morgan upset at 159-degree temps | Transfer photos
Kurt, a Germany Under-18 international, enjoyed a prolific 2013-14 campaign netting 16 goals to help his side to a sixth-placed finish and his efforts have earned him a four-year deal with Pep Guardiola's men.
"One of the biggest German talents moves to Bayern," the reigning German champion said in a statement on the Bayern website. "Borussia Monchengladbach's Sinan Kurt signed on a four-year contract on Sunday with the German champions after both clubs had previously agreed a transfer agreement."
Considering the vast array of talent at the Allianz Arena, Kurt is highly unlikely to be part of Bayern's first-team squad in the immediate future.