The 33-year-old right-hander had signed a minor league contract with the Mariners in January but was released on Sunday after throwing just four innings this spring.
He appeared in 32 games for the Diamondbacks last season, amassing an unsightly 6.88 ERA and 1.670 WHIP in 35 1/3 innings.
Heilman had a solid three-year stint from 2005-2007 as a reliever for the New York Mets, putting up a 3.27 ERA, 7.8 K/9 and 1.128 WHIP in an average of 94 innings, but has struggled in the four seasons since then.
For his career, which now spans nine seasons, Heilman has a 4.40 ERA, 3.7 BB/9, 7.8 K/9 and a 1.362 WHIP.
He has been assigned to the Rangers' Triple-A affiliate in Round Rock, Texas.
Rangers Sign Heilman | Twitter @aandro
Rangers sign Aaron Heilman to minor-league deal. Assign him to Round Rock.