Howry, 36, still gets the $2.25 million he was due from the Diamondbacks this season. He had a 10.67 ERA, worst on the staff, and had allowed six home runs in 14 relief appearances. In Arizona's 13-1 loss at Atlanta on Sunday, Howry gave up a home run to Troy Glaus on his first pitch and did not retire any of the five batters he faced.
Rivera, also a right-hander, was acquired from the Indians for cash considerations.
Rivera was 2-0 with four saves and a 0.53 ERA during 15 relief appearances for Triple-A Columbus. He was signed by the Indians to a minor league contract on Dec. 21.
Rivera has played part of 13 seasons professionally, including four seasons with the Washington Nationals from 2006-09.
The Diamondbacks are recalling right-hander Billy Buckner to start at Florida on Tuesday.