The 34-year-old Stuart will help bolster the Avalanche's blue line after a season in which he skated in 61 games for the Sharks. He was third on the team in blocked shots (114) and hits (122).
Stuart was the third overall pick by San Jose in 1998. He's also suited up for Boston, Calgary, Los Angeles and Detroit.
Colorado has been active the last two days, acquiring veteran forward Daniel Briere from Montreal on Monday for right wing P.A. Parenteau and a fifth-round pick next year.
Earlier Tuesday, the Avalanche lost Paul Stastny through free agency as the center signed a four-year deal with St. Louis.