The 53-year-old Spaniard replaces Christophe Galtier, who has been sacked despite winning the Ligue 1 title in his one season in charge.
Luis Enrique has signed a two-year contract with the French champions.
It is his first role since he stepped down as Spain manager in December after defeat by Morocco on penalties in the last 16 of the 2022 World Cup.
His last job in club management was at Barcelona, where he won nine trophies in three seasons between 2014 and 2017, including the Champions League, La Liga and Copa del Rey Treble in his first campaign in charge.
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