Spaniard Ramos, 54, who was sacked as Tottenham coach in October after the English side's worst start to a Premier League season, agreed a contract through June 2009 with an option for an extension, sporting director Predrag Mijatovic said.
Mijatovic told a news conference at the Bernabeu stadium that he had met Schuster earlier on Tuesday and the pair had agreed the German's contract with the Primera Liga champions should be terminated.
Former Real player Schuster took over from Italian Fabio Capello in June 2007 and helped them to a second straight title. However, this season his side have slipped nine points behind arch-rivals Barcelona this term.
"I met with Schuster this morning and we discussed the problems of the past weeks and months and by mutual agreement took this decision," Mijatovic said. "I am more than convinced we have made a good decision."
Ramos will take immediate charge of the side, who have a home Champions League tie against Zenit St Petersburg on Wednesday and travel to play Barcelona at the Nou Camp on Saturday for "El Clasico".
They have already qualified for the knockout stages of Europe's top club competition but are fifth in the league after 14 matches. They lost 4-3 to Sevilla at home on Sunday.
Speaking at the news conference with Mijatovic, Ramos said it had been impossible for him to reject Real's offer and he was excited about the new challenge.
"This is the dream of all soccer coaches," he said. "Real Madrid has the quality to win in any stadium in the world and they must go into every match thinking of victory."
INJURY PROBLEMS
Real have been plagued by injuries and suspensions this season and Schuster said after the Sevilla defeat that it would be impossible to win at Barcelona at the moment.
"They are devastating. I think it is their year," he said. "We will try to put on a good show. We won't be able to do more than that."
Schuster's comments were variously interpreted either as mind games ahead of the clash or an effort to motivate his players but they did nothing to ease the pressure on president Ramon Calderon, Mijatovic and himself.
Ramos was replaced at Tottenham by Harry Redknapp after they failed to win any of their first eight matches. Spurs had won only six times in 26 attempts in all competitions since the Spaniard led them to the League Cup in February.
He enjoyed more success at Sevilla, taking over from Joaquin Caparros in 2005 and winning five trophies in two years including back-to-back UEFA Cups.
Ramos of Real: A potted history
Real Madrid: 11 coaches in 10 years
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