Germen, 27, had spent his entire career with the Mets and appeared in 54 games for them over the past two seasons. He has a career record of 1-2 with a 4.31 ERA and an opponents' batting average of .248.
Germen averages 8.6 hits, 4.2 walks and 8.9 strikeouts per nine innings. His repertoire consists of a 92-mph fastball with a slider and a changeup.
"He has a plus fastball with some moving parts in a slinging delivery and a good changeup," Rangers pro scouting director Josh Boyd said.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.