Cancelo made 16 league starts for City this season but has not played for the club since their derby loss to Manchester United earlier this month, missing the last three games.
He started only three of 10 games after the World Cup break and lost his place to Nathan Ake while 18-year-old Rico Lewis also emerged as an option for manager Pep Guardiola this season.
"We've signed him on loan now and have the possibility of signing him permanently in the summer," said Bayern's sports director Hasan Salihamidzic.
"Joao is a player we've been thinking about for a while now because we very much appreciate his qualities. He's the optimal fit in our system with his attacking style of play and dynamism, and his mentality and experience fit very well in our team."
Cancelo has been instrumental for City since his arrival in 2019, winning two league titles, while he was also named in the Premier League Team of the Year in the past two seasons.
The versatile 28-year-old has predominantly played as a left back but can also operate on the right flank.
"FC Bayern is a great club, one of the best in the world, and it's enormous motivation for me to now play alongside these extraordinary players in a team," Cancelo said.
"I know that this club, this team lives for titles and wins titles every year. I'm also driven by the hunger for success. I'll give my best for FC Bayern."
Bayern top the Bundesliga but have failed to win since the restart after the World Cup. They have had three straight draws and their lead over Union Berlin has been cut to a point.
