The 34-year-old was released by AC Milan at the end of last season after 13 years at the Serie A club.
He had been linked with a return to former employers Rangers, but the uncertainty surrounding their future prompted Gattuso to look elsewhere.
Sion announced the player's arrival on their website, and will present him at a press conference later on Friday.
Gattuso twice won the Serie A title with Milan, as well as two UEFA Champions League trophies. He was also a member of Italy's FIFA World Cup™-winning squad in 2006.