City will pay a net fee of €28 million with Cancelo's move valued at €65 million and Danilo costing €37 million.
"City are a fantastic club, with a brilliant manager and I am delighted to be here,” said Cancelo, who signed a six-year contract.
"Everything about them has impressed me, from the facilities, to their style of play.
"I am always looking to develop my game and win trophies and I believe I can do that here, so now I'm really looking forward to the new season and testing myself in the Premier League."
Cancelo won one Serie A title with Juventus after a €40 million move from Valencia last year.
"Joao is a fine player and an excellent attacking full-back who will provide us with a real threat on the right-hand side," said City director of football Txiki Begiristain.
"He fits the profile of player we want here at Manchester City. His best years are ahead of him, he's technically proficient and has the physical attributes we desire."
Danilo was part of the City squad that has won five domestic trophies in the past two seasons, but has played second fiddle to Kyle Walker at right-back.
"It's been a pleasure to be part of the success City have enjoyed in my time here," said Danilo, who has signed a five-year contract with Juventus.
"The club have been fantastic with me from day one and I will always be grateful.
"The Premier League title wins will stay with me forever and I will always have City in my heart."