He is due to be officially presented in the Bernabeu at 1700 GMT.
"We consider him to be in perfect condition to sign for Real Madrid so we have given him the OK," Real doctor Alfonso del Corral told the club's Web site.
Real said they had reached an agreement with United to sign the 30-year-old on Thursday, though United said on their Web site the terms of the deal had yet to be finalised.
No fee was officially disclosed but Spanish media reported it to be worth around 15 million euros ($19.12 million).
He is Real's third signing under new president Ramon Calderon following on from Italy defender Fabio Cannavaro and Brazil midfielder Emerson, and will link up with former Manchester United team mate David Beckham.
Van Nistelrooy, who scored 20 goals or more in four of his five seasons at Old Trafford, put in a transfer request two weeks ago and Real beat Bayern Munich in a tug-of-war to secure his services for next season.
After having fallen out of favour with United manager Alex Ferguson, Van Nistelrooy now faces the challenge of competing with Raul, Robinho, Julio Baptista, Antonio Cassano and Ronaldo for a place in the Real attack.
