Olson, who has nine years experience in the NFL, was San Francisco's quarterbacks coach last season and served as Arizona's offensive coordinator from 2001-02.
Olson will replace Scott Linehan and work closely with Daunte Culpepper, who set several team records in 2004 and made his third Pro Bowl. Culpepper's career took off under the tutelage of Linehan -- who left to become Miami's offensive coordinator.
Vikings offensive line coach Steve Loney was promoted last month to replace Linehan as offensive coordinator.
Coach Mike Tice is still searching for a wide receivers coach to replace Charlie Baggett, who joined Linehan with the Dolphins.