The move is retroactive to Thursday and comes after the team opted to skip the two-time All-Star's turn in the rotation to give its starters some rest.
Eovaldi, 33, has posted an 11-3 record with a 2.69 ERA in 19 games (all starts) this season.
He is 78-71 with a 4.03 ERA in 259 career games (240 starts) with the Los Angeles Dodgers (2011-2012), Miami Marlins (2012-2014), New York Yankees (2015-2016), Tampa Bay Rays (2018), Boston Red Sox (2018-2022) and Rangers.
Texas recalled right-hander Grant Anderson from Triple-A Round Rock in a corresponding move.
Anderson, 26, is 1-1 with a 5.20 ERA in 19 relief appearances with the Rangers this season.
Information from Reuters was used in this report.