The 21-year-old moves to Italy for an undisclosed fee with British media reports claiming he has signed a four-year-deal with the Serie A club.
Suso failed to establish himself at Liverpool after joining in 2010, making 21 appearances for the club, and spent the 2013/14 season on loan at Almeria in Spain.
Filippo Inzaghi's Milan are eighth in the league table, five points adrift of third-placed Lazio and a Champions League qualifying place.
(Reporting By Sam Holden; editing by Amlan Chakraborty)
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