Harvey will join the Reds later this week in Los Angeles. The Reds also selected the contract of catcher Tony Cruz from the Triple-A Louisville Bats in a corresponding transaction.
New York also placed Todd Frazier on the 10-day disabled list, due to a left hamstring strain. The Mets transferred Anthony Swarzak to the 60-day disabled list in order to make room on the 40-man roster.
Mesoraco, 29, is hitting .220 this season with a home run and three RBIs. The 2014 National League All-Star is a career .234 hitter in his eighth season with the Reds. Mesoraco was the No. 15 overall selection in the 2007 MLB June Amateur Draft.
Harvey, 29, had a 7.00 ERA and 0-2 record in eight appearances this season for the Mets. The 2013 All-Star went 5-7 with a 6.70 ERA in 19 appearances last season. Harvey is due $5.62 million this season and is a free agent in 2019. Mesoraco is also a free agent in 2019. He has a $13.1 million salary in 2018.
The Mets designated Harvey for assignment on May 4 after he refused a request from the Mets to go to the minors. Harvey was previously demoted to the bullpen in 2018 after he struggled as a starter.