The embattled tackle, who was most famous in Chicago for being bumped and yelled at by quarterback Jay Cutler during a Thursday night game in 2012, was released by the Bears on Saturday.
Webb moved from left tackle to right tackle last season, and would give the Vikings a backup option at both positions.
Of the three backup offensive linemen who made Minnesota's roster on Saturday, only Troy Kropog projects as a backup tackle.
All five Vikings offensive linemen started all 16 games last season, so while the team has little reason to be concerned about its durability on the offensive line, Webb provides some depth in case of an emergency.
ESPNChicago.com's Jeff Dickerson contributed to this report.