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Real sports director Pedja Mijatovic said he had held an earlier meeting with Schuster, at which the German "accepted" the decision but "was sad to do so".
According to Real, Ramos has been given an initial six-month deal at the Spanish giants.
Schuster’s head was placed firmly on the block on Sunday when Real slipped to a humiliating 4-3 home defeat to Sevilla, a result that left them languishing in fifth place in the league, nine points behind leaders
The German coach had been under pressure as early as November following elimination from the Kings Cup by third-division Real Union.
But it appears the final nail in the coffin was Schuster’s remarks to the Spanish press last weekend, when he said his injury-riddled side had no chance in next weekend's game in the Nou Camp against arch rivals
Ramos was sacked as manager of Tottenham in October following a disastrous start to the season that saw the Londoners bottom of the Premier League, but he enjoys a healthy reputation in