Ramirez pitched 18 games with the Phillies in 2013, spent '14 in the Indians' Minor League system and appeared in 12 games with the D-backs this season, recording a 4.11 ERA. Most of his time this year has been spent with Triple-A Reno, where he posted a 2.88 ERA.
Ramirez will report to Tacoma on Tuesday.
The 6-foot-4, 250 pounder was dealt to the Phillies along with outfielder Tyson Gillies and right-hander Philippe Aumont. In 10 seasons in the Minors, Ramirez is 50-57 with a 4.19 ERA.
He was a starter in his initial years, but switched to a relief role in 2012.