Memphis also waived big man Jordan Bell.
Tolliver became a free agent earlier this week after reportedly agreeing to a buyout with the Sacramento Kings. He was officially waived on Saturday.
The 34-year-old received offers from multiple teams after parting ways with the Kings, according to Shams Charania of The Athletic. Tolliver owns a career 37.3% mark from beyond the arc and is expected to serve as a stretch-four off the bench in Memphis.
Bell started this season with the Minnesota Timberwolves but was traded to the Houston Rockets along with Robert Covington in a four-team deal one day before the deadline. On deadline day, he was shipped to the Grizzlies in exchange for Bruno Caboclo and a second-round pick.