Schuster will take over for Fabio Capello, who was fired on June 28, less than two weeks after leading Madrid to its first Spanish league title in four years and ending the club's longest major trophy drought in 53 years.
The former Germany defender has coached Getafe since 2005. The Madrid-based club lost 1-0 to Sevilla in the Copa del Rey final and finished ninth in the league.
Schuster will be Madrid's eighth coach in four years.
Club president Ramon Calderon said recently Madrid was considering offering the job to Arsene Wenger, Ronald Koeman or Michael Laudrup. But news reports said Calderon had wanted Schuster even before the club signed Capello last year.
Schuster, 47, is a former star for Madrid, FC Barcelona and Atletico Madrid.
Besides Getafe, Schuster has also coached Spain's Levante - which he led to promotion to the first division in 2004 - Germany's Cologne, Spanish second-division side Xerez, and Ukraine's Shakhtar Donetsk.
The behavior of the Russian inspector satellite, which was launched in the autumn of 2017, puzzles military officials in the United States
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