Rivera agreed to a one-year, $1 million contract with the Orioles on Friday to avoid arbitration, Mark Feinsand of MLB.com reports.
Rivera went 4-for-4 with two home runs, a double, a walk, four RBI and three runs scored in Saturday's 9-2 win over the Twins.
Rivera is out of the lineup for Sunday's game against the Tigers.
Rivera will start at third base and bat seventh in Wednesday's game against the Giants.
Rivera will start at third base and bat ninth in Monday's game versus the White Sox, Roch Kubatko of MASNSports.com reports.
Rivera went 2-for-3 with a home run and three RBI in Friday's 5-3 win over the Rockies.
The Orioles claimed Rivera off waivers from the Marlins on Wednesday.
The Marlins designated Rivera for assignment Monday.
Rivera is out of the lineup for Sunday's game against the Padres.
Rivera isn't in the Marlins' lineup Saturday versus the Padres.