Benedicic, 18, is an attacking midfielder and he moves to Elland Road on a season-long deal.
The Slovenia Under-21 international has yet to make a competitive senior appearance for Milan but played a major part in the club's Under-19 campaign last season, making over 30 appearances.
He becomes Leeds' latest acquisition from an Italian club this summer following the arrivals of goalkeeper Marco Silvestri, defender Gaetano Berardi, midfielder Tommaso Bianchi and striker Souleymane Doukara.
United head coach Dave Hockaday told the club's official website: "Zan is a versatile, strong and technical midfield player. He has massive potential and comes highly recommended by AC Milan."
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