The experienced duo have confirmed they will be exiting San Siro at the end of the season after more than a decade of service at the Serie A giants
Both players have expiring contracts with Milan and will depart San Siro after a season in which they featured infrequently.
This is the third Milan veteran to wave goodbye to the club after Alessandro Nesta revealed on Thursday that he will quit the Rossoneri in the summer.
Gattuso, who joined Milan from Salernitana in 1999, has made only six appearances this season after a serious eye problem forced him to spend several months on the sidelines.
He said earlier in the week that he could retire from football if he was not guaranteed an active role at Milan next season.
"I leave because the time has come for me to give room to other players," he told reporters.
"I will explain everything at a press conference on Saturday. I do not know yet where I will go, I have not yet decided."
Inzaghi, 38, has been at Milan since 2001, when he joined the club from Juventus, scoring 125 goals in 296 appearances for the Rossoneri but featured just eight times this season.
"Today I would like to thank with affection and emotion president Berlusconi and Adriano Galliani," Inzaghi said in a open letter, published on Milan's website.
"Their electricity and their ability to transmit emotion made me stronger and pushed me beyond any and all limits.
"But I also want to give a thought to those who, from the youth sector to all the wonderful clubs that I’ve played for, helped me to become the man and the player that I am today.
"Thank you Milan, thank you football. Allow me to call you my own, the people of Via Turati, from Milanello to the offices to the phone operators to the warehouse workers, the physiotherapists, the doctors, the cooks, from the stadium to the changing room.
"All the people who saw me on Sunday with the short sleeves and shook with the hope that I would score.
"Ciao Carlo Ancelotti, I won a lot with you, ciao to my wonderful fans who followed me the world over with affection and passion. Ciao to my team-mates from today and yesterday."
More players could join the Milan exodus in the next few days, as seven other footballers have expiring contracts with the Rossoneri.