The 18-year-old has been bought off Bundesliga rivals Borussia Monchengladbach, though the selling club are disappointed with his decision to leave so soon in his career
The midfielder, 18, is yet to feature in a first-team league match, but made 24 appearances in the Under-19 Bundesliga for Gladbach last season.
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 talent moves to Bayern," the reigning German champions said in a statement on their 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."
Gladbach sporting director Max Eberl is disappointed that Kurt decided against extending his contract at Gladbach and feels a longer stay at the club would have proved beneficial.
"It is significant for our excellent junior work, when Bayern are so vehemently interested in one of our talents," he said. "We are of the opinion that this would have been the best way for him."
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 and is expected to continue his development .