The Portuguese was sacked and replaced by Sergio Conceicao at AC Milan on Monday.
Fonseca cleared out his office in the afternoon at Milanello, before later sending a message to Milan fans.
He posted: "The time has come to say goodbye. I am proud to have worked for Milan and I have always given my heart and soul to honor the history and tradition of this great club.
"I would like to thank my staff, the players, the fans and everyone who supported me during my time in Milan. I wish the club all the best for the future."