Stanway was just 16 when she made her debut for Man City and leaves as the club’s top goalscorer with 67 goals in 186 appearances.
The 23-year-old England forward, who was out of contract with Man City this summer, signed a three-year deal with Bayern.
Reacting, Stanway was quoted by BBC Sport as saying on Tuesday, “It just feels right,” she said. “I can’t wait to get started and play for such a well-known club.”
“Bayern has very big ambitions and I really admire that,” she added.
Stanway won the FA Women’s Super League (WSL) in 2016 as well as three League Cups and three FA Cups during her time with Man City.