The Argentinian midfielder has agreed a four-and-a-half year deal, according to Malaga's website.
He leaves Malaga after scoring five goals in 31 appearances in La Liga, the Copa del Rey and the Champions League.
A statement on the Malaga website said: "Malaga Club de Futbol
is grateful for Buonanotte's professional, hard-working attitude during his time at the club, and wishes him every success with Granada."
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