Bayern have been pursuing the Germany international for some time and have announced they had agreed an undisclosed fee with City with the player having successfully negotiated a four-year deal at the Allianz Arena.
The 22-year-old joined City last summer from Hamburg but struggled to make an impact due to a succession of injuries. The deal will be completed once Boateng has passed a medical in Bavaria.
A statement on the Bayern website read: "The board of Bayern Munich and the board of Manchester City have reached an agreement for the transfer of Jerome Boateng.
"Boateng, who is currently with City in Los Angeles, is expected in Munich in the next few days for a medical.
"Then he will sign a contract up to June 2015. The clubs have agreed not to disclose the transfer fee."
Bayern chairman Karl-Heinz Rummenigge was delighted to have finally landed Boateng.
"There have been some intense negotiations and we have come a long way to reach a satisfactory conclusion," he said on the club's official website, www.fcb.de.
"With Jerome Boateng we have got our preferred candidate to play in central defence for Bayern Munich."
Bayern sporting director Christian Nerlinger added: "Jerome Boateng is a young Germany international who fits perfectly into the philosophy of Bayern. He was also wanted by our coach Jupp Heynckes."
Source: PA
Source: PA