The 28-year-old arrived in Munich on Monday before undergoing a medical with the Bundesliga club.
He has now joined on loan until the end of the season, although the deal includes an option for them to buy Cancelo for £61.6million at the end of the season.
Relations between Cancelo and Guardiola have deteriorated, and reached a head when the full-back was left out of the City team for their FA Cup win over Arsenal last Friday. Cancelo has become increasingly frustrated with his lack of playing time.
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Under UEFA rules, Cancelo will be free to face City in the Champions League should the two teams meet in the competition this season.
Taking to Instagram, the former Inter Milan defender wrote: “Once a Cityzen, always a Cityzen. Thank you.”
Bust up: Cancelo and Guardiola are believed to have fallen out, paving the way for his move to Bayern
/ AFP via Getty ImagesBayern sporting director Hasan Salihamidzic said: “We’re very happy that Joao Cancelo will now play for FC Bayern. We’ve signed him on loan now and have the possibility of signing him permanently in the summer.
“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. I’m convinced João will help us in the coming weeks and months where we want to win titles.”
