Wacha spent the 2020 season with the New York Mets, going 1-4 with a 6.62 ERA in eight appearances (seven starts).
The 29-year-old Wacha shined as a rookie for the St. Louis Cardinals in 2013, winning National League Championship Series MVP, but has been frequently injured since, including missing time last season with shoulder inflammation.
Wacha spent his first seven major league seasons with the Cardinals and was an All-Star in 2015. He has a 60-43 career record with a 4.01 ERA.
The Rays also announced that they have agreed to terms with right-hander Chris Ellis on a minor league contract with an invitation to major league spring training. Ellis has one inning of major league experience, in 2019 with the Kansas City Royals.
Morton signed a one-year, $15 million contract with the Atlanta Braves last month after Tampa Bay declined his $15 million option. The 37-year-old joined the Rays in 2019 and helped Tampa Bay reach the playoffs the past two seasons. The right-hander was 3-1 with a 2.70 ERA during this year's postseason.
Wacha's signing also comes one day after the Rays announced that right-hander Brent Honeywell had arthroscopic elbow surgery that is not expected to affect his 2021 season.
The Associated Press contributed to this report.