The 6-foot-8 power forward will return for a second stint with the Wolves, having played for the team in 2010-11 and 2011-12.
Tolliver played for the Detroit Pistons in a reserve role last season and averaged 8.9 points, 3.1 rebounds and 1.1. assists in 22.2 minutes per game.
The 33-year-old journeyman has played for nine franchises since entering the league in 2008.
News of Tolliver's agreement with Minnesota came on the same day that the franchise rescinded its qualifying offer to Nemanja Bjelica, sources told ESPN's Adrian Wojnarowski.
The maneuver makes the 6-10 power forward an unrestricted free agent.
Bjelica, 30, averaged 6.8 points and 4.4 rebounds and shot 41.5 percent from behind the arc.