The 24-year-old joined Malaga from River Plate in January 2011, but never quite managed to live up to the high expectations that came with his arrival.
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Buonanotte had become surplus to requirements at the Boquerones following the arrival of Lucas Piazon on loan from Chelsea earlier this month, and was therefore allowed to move on when the opportunity arose.
The attacking midfielder made 31 official appearances for Malaga over the past two years, netting five goals in the process.
Granada were desperate to add some fresh blood to their squad, as they are battling against relegation this season after winning promotion to Spain's top tier last term. They currently sit 17th in the Liga table.