The veteran midfielder was a free agent after Milan allowed his contract to expire this summer and has now signed a two-year deal with Sion.
"In talking to the President, we agreed that we were looking for a central midfielder," explained director of sport Marco De Gennaro on Sky Sport Italia.
"At that point I said we needed someone like Gattuso, so the President asked 'why not the real Gattuso?'
"I asked his agent if such a thing could be worked out, but he told us it was impossible. Gattuso turned down plenty of proposals, but we slowly started talking and the deal went through."