The Rays selected Heasley's contract from Triple-A Durham on Wednesday.
Heasley had been serving as a swingman at Durham this season, making seven appearances (four starts) while logging a 3.90 ERA and 1.21 WHIP across 27.2 innings. Though he could eventually be an option in the Tampa Bay rotation, for the time being, Heasley is expected to settle into a bullpen role. He'll give the Rays another arm who's capable of covering multiple innings after Tampa Bay placed Jesse Scholtens (wrist) on the 15-day injured list Tuesday.