The Rossoneri official was relieved to see the club hold on to the Brazilian stopper, while revealing that Gattuso rejected their offer of an extension.
The Italian giants had opened talks with PSG after receiving an offer worth 46 million euros from the French capital club, with a deal understood to be close at hand.
However, Milan has announced that it will not let Thiago Silva leave, and the French club later confirmed that negotiations with the Rossoneri had broken down.
"I feel much better now, after president Silvio Berlusconi's decision," Galliani told Azzurra Italia. "If the fans are happy? I am also a fan of this club.
"We have to thank Berlusconi. This was an act of heroism. We will lose a lot of money by keeping Thiago Silva, but Berlusconi will pump that money into the club himself.
"Zlatan Ibrahimovic? Of course that he will stay. We are fully covered in all areas."
Galliani was then asked about former Milan midfielder Gennaro Gattuso as the 34-year-old is on the verge of joining Swiss side Sion.
"Gattuso to Sion? If you have to ask him because he could have renewed his contract," the Milan official revealed. "But he chose to go in a different direction and you have to respect him."
Follow GOAL.COM USA on