Gattuso, who has been in charge for 18 months, led Milan to fifth place in Serie A this season, missing out on a berth in next season's Champions League by one point.
The 41-year-old has been under enormous pressure during his time in charge, with speculation over his future repeatedly popping up during the course of the season.
Gattuso, a combative former midfielder who spent most of his career with Milan, had never coached a Serie A side before he was appointed in November 2017 to replace Vincenzo Montella.
He led them to sixth place last season and the Coppa Italia final, where they lost to Juventus.
This season, they were beaten by Lazio in the Coppa Italia semi-finals and knocked out of the Europa League in the group stage.
However, the biggest disappointment was their failure to qualify for the Champions League, meaning that Milan will now be absent from the competition they have won seven times for the sixth season in a row.
(Reporting by Elvira Pollina and Brian Homewood, editing by Giselda Vagnoni/Peter Rutherford)
