The former Sion midfielder has praised the Rossoneri icon's positive influence during his time at the club and believes he will not be forgotten any time soon
Ambrosini's time at Milan comes to an end this summer after 18 years and Gattuso has applauded the 36-year-old's positive influence at the Rossoneri over the years.
"Ambro will always be part of Milan's history. He was a great team-mate and a great captain," the new Palermo coach told Sky Sport.
"He was also a great athlete and, without all of his injuries, he had he could have done a lot more.
"I was a little sad for Ambro when I heard about his departure, but Milan's politics these days is centered around building a young team and you have to respect that."
Gattuso said farewell to Milan in the summer of 2012 after a 13-year spell.
He spent last season at Sion - as a player and subsequently a player-manager - and was appointed Palermo coach this week ahead of the 2013-14 Serie B campaign.