Strop, 34, was part of the Chicago Cubs' bullpen the past six years. A hamstring injury limited him to 50 appearances last season, when he went 2-5 with a 4.97 ERA, 10 saves and six blown saves.
Strop had a rough middle of the season after returning from the injury. He went 1-1 with four blown saves in July and 0-1 with a 9.00 ERA and one save in August. He finished strong, putting up a 2.00 ERA in 11 appearances in September.
Cincinnati has committed more than $165 million on acquiring players this offseason, including the two biggest free-agent contracts in club history.
Cincinnati signed second baseman Mike Moustakas to a four-year, $64 million contract and added left-handed starter Wade Miley on a two-year, $15 million deal. Outfielder Shogo Akiyama, an All-Star in his native Japan, got a three-year, $21 million agreement. Outfielder Nick Castellanos also reached a four-year, $64 million deal that includes player opt-outs after 2020 and 2021.
Strop will get a chance to pitch in a setup role to closer Raisel Iglesias, who had 34 saves last season. Cincinnati's bullpen finished seventh in the National League with a 4.28 ERA and a 27-33 record.
To make room for Strop, the Reds designated right-hander Sal Romano for assignment.