Garrido has one year left on his contract with Real, but will join City in a deal worth around £2million.
Real boss Chris Coleman: “He is a good player, but Manchester City has an interest in him and it is the decision of the player to go to England.
“I have explained to him that I do not want to sell him, but the financial situation is what it is.
“We do not want to lose him but it is his decision. Both clubs have an understanding over money.
“In the end the deal for Garrido, whatever the price, will help us in other areas and we have to be clever.”