The midfielder is being allowed to come off contract this month.
"It is a real shame to say goodbye to Ambro, a decision that seems me very emotionally involved," Galliani told Milan Channel.
"I apologise to Massimo once again in case we hadn't already told him the decision. We've been torn for many days.
"He too is very disappointed, but at the end of the day age proved more important than emotions. Ambrosini has been a great Milan player, having 18 seasons with us is incredible.
"In 18 years a baby is born and grows into a man, so he achieved so much with us. I think it might be a record that he won four Scudetti with four different Coaches: 1995 with Fabio Capello, 1999 with Alberto Zaccheroni, 2004 with Carlo Ancelotti and 2011 with Massimiliano Allegri."