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Luxemburgo has a wealth of experience after coaching the Brazilian national team and a number of top Brazilian club sides.
He has won the Brazilian championship a record five times with four different clubs and helped Santos to win this season's title.
"Real Madrid's board has unanimously approved the proposal of the sports management team to appoint Wanderley Luxemburgo as new coach," said Real vice-president Emilio Butragueno.
"It's not been an easy decision for us but we think it is the best decision right now for Real Madrid."
Roberto Carlos has welcomed the appointment of Wanderley Luxemburgo as the new coach of Real Madrid and believes he can turn things around at the club.
The Brazilian international could not hide his delight after his former trainer at national and club level took over from Mariano Garcia Remon during this week.
"I have known him for around 12 years now," Carlos explained. "I played under him at Palmeiras and with the Brazilian national team.
"I could spend a lot of time talking about everything that he won and achieved in his career, but you will tell me I speak too much if I do.
"He has his own style of doing things and likes his teams to be happy when they play. He is a winner and I am sure he will make us into champions.
"In Brazil everyone is accustomed to training twice a day and he will do that, starting next week when we are due to work in the morning and afternoon. The team will improve physically and tactically."