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The 21-year-old former Manchester City player has been handed the number 21 shirt at theRossoneri.
"AC Milanis delighted to announce the signing of the Spanish footballerBrahim Abdelkader Díazfrom Real Madrid CF on loan untilJune 30, 2021," read a Milan statement.
Diaz only joinedjoined Madrid in January 2019 after six years atManchester Citybut has struggled for regular opportunities.
The former Malaga youngster, who joined City as a 16-year-old in 2015, has made just fiveLa Liga for Los Blancos and was restricted to just sixsubstitute appearances in the top-flight last season.