In a statement, Los Blancos said: "The club would like to thank the player for his professionalism, commitment and dedication throughout his time at Real Madrid and wishes him all the best in this new stage of his career".
"I am very, very happy to be joining Manchester City", said Danilo, whose move is subject to his receiving his work permit.
'I am sure that over the next few years we will be successful'.
City were in desperate need of full-backs with all four of last season's options in Bacary Sagna, Pablo Zabaleta, Gael Clichy and Aleksandar Kolarov having left the club this summer.
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It is not right to take such action without passing any notice or conducting any enquiry, ' adding, "other parties are with us". And unable to understand why this happened, as I did not prevent them from raising any issue.
One player who is back at the Etihad Stadium is midfielder Yaya Toure after agreeing a new one-year contract to remain at the club.
These calculations do not include Bernardo Silva, who was signed from Monaco at the beginning of the summer transfer window and could well be a jewel in City's crown. The Frenchman became the champion of France, entered in the symbolic team of the season in League 1, played in the semi-finals of the Champions League and debuted in the national team.
With sky-blue trim on the shirt and socks, the latest in a long line of maroon kits offers a nod to City's league title-winning side of 1967/68. In fact, Mendy has made more accurate crosses from open play (116) than any other Ligue 1 player since August 2014.
The deal took a while to complete, but City's director of football, Txiki Begiristain, was pleased to have secured their first-choice target."Benjamin has all the qualities we are looking for in a full-back". In, The Sun claims transfer talks with PSG have broken down, while The Times report that City will bid £50m if Arsenal change their stance and allow the Chilean to leave.
It means that yet another member of that thrilling Monaco squad from last season has left the Stade Louis II.