Filippo Inzaghi, 41, who played for AC Milan from 2001 until his retirement in 2012, replaced former team-mate Clarence Seedorf in the post last June. On Tuesday morning he was sacked from the managerial position and has already been succeeded by Sinisa Mihajlovic.
According to Gazzetta dello Sport, Mihajlovic met AC Milan president Silvio Berlusconi late on Monday, with terms thrashed out over dinner.
The Serb stepped down as Sampdoria manager on Monday after guiding the Genoa-based club to seventh - three places above AC Milan - which he will hope to improve upon again next season.
The 46-year-old took charge at Sampdoria in November 2013 and has previously managed Bologna, Catania, Fiorentina and Serbia and played at full-back for Sampdoria, Lazio and Internazionale over the course of a distinguished career.
Due to financial limitations, AC Milan are no longer able to buy the world's best players and have, therefore, struggled for several seasons. The last time they won the Serie A title was in 2011 under the management of Massimiliano Allegri – a man now overseeing matters at reigning champions and Champions League finalists Juventus.