Both clubs confirmed the deal on Sunday morning after the 26-year-old Brazil global left Real's pre-season camp in Los Angeles to undergo a medical with the Premier League side this weekend.
The 26-year-old has joined City on a five-year contract and will immediately link up with Pep Guardiola's squad in the United States, where he may make his City debut in the International Champions Cup.
Left-back Benjamin Mendy is also set to join from Monaco after City allowed Aleksandar Kolarov, Pablo Zabaleta, Gael Clichy and Bacary Sagna to leave the club.
"We have many options for people, players coming, but until the deal is done out of respect for the other clubs I can not say absolutely anything", he said.
However, City's attempts to sell him have been complicated by the UEFA probe after it emerged that he visited the Drip Doctors clinic in Los Angeles in December and may have received intravenous treatment that could breach doping rules.More news: Energy Transfer Equity, LP (NYSE:ETE) Stake Lowered by Grassi Investment Management
Danilo had been with Real since 2015, and played 24 matches for Zinedine Zidane's side last season as they won the Spanish league title, sealed their second consecutive Champions League trophy and won the Club World Cup.
"I can't wait to get started and I'm looking forward to getting to know my new team-mates over the coming weeks".
The France global, 23, was putting the finishing touches to his £49.3m switch from Monaco. "I just hope to help him out as he expects". He can play at both right-back and left-back as well as in midfield.
'You have to learn how to win and I love winning.