The Rays made the move Monday. Tampa Bay is in the thick of the races for the AL East and the wild-card spots.
Wright is expected to join the Rays for Tuesday night's home game against Seattle.
The 28-year-old Wright is 0-4 with a 3.92 ERA and leads AL relievers with 54 appearances. He has struck out 40 in 41 1-3 innings with 16 walks.
Wright pitched in 77 games last year. He has spent six seasons in the majors, all with Houston, and was the longest-tenured player on the last-place Astros.