Schuster, 53, comes in to replace Manuel Pellegrini, who said he was leaving the Spanish club last month and is widely expected to be appointed as the new coach at Manchester City.
Local media have reported that Schuster's appointment was being held up until the club finally agreed the ending of their agreement with Pellegrini.
Malaga said in a statement on their website that they would present Schuster, who had agreed a five-year contract, as their new coach next week,
The former West Germany midfielder spent most of his playing career in La Liga with Barcelona, Real and then Atletico Madrid.
He coached in Spain, with second division Xerez and top-flight sides Levante and Getafe, before he took over at Real Madrid as Fabio Capello's replacement in 2007.
Schuster guided the nine-times European champions to a second successive league title in 2008 but was sacked midway through the following season.
He took over at Turkish side Besiktas in June 2010 but quit the following March, continuing a pattern of inconsistent, short spells as a manager, and has not coached since then.
Chilean Pellegrini led Qatar-owned Malaga to a sixth-placed finish in La Liga and to the quarter-finals of the Champions League in their debut campaign in the competition.
Malaga should have qualified for next season's Europa League but they have been banned from European competition for a season because of overdue payments to rivals clubs and the Spanish tax authorities.
An appeal against the ban was rejected by the Court of Arbitration for Sport (CAS) on Tuesday.
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