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12/30/11 5:17 PM EST

Free-agent reliever Oliver signs with Toronto

ARLINGTON -- The Rangers have lost pitcher Darren Oliver to the Toronto Blue Jays.

The veteran left-handed reliever, who is represented by former Rangers infielder-turned-agent Jeff Frye, agreed to a one-year contract with the Blue Jays on Friday, according to industry sources.

Oliver's departure leaves the Rangers without a proven left-handed reliever in their bullpen.

The deal is pending a physical. The Rangers will receive a supplemental first-round Draft pick as compensation.

Right now, Texas is looking at an all right-handed bullpen that would include closer Joe Nathan and Mike Adams, Mark Lowe, Koji Uehara and Yoshinori Tateyama as the setup men. Michael Kirkman is also on the 40-man roster. Kirkman had a 1.65 ERA in 14 games for the Rangers in 2010 and a 6.59 ERA in 15 games this past season.

The Rangers have some interest in free-agent left-handed reliever Michael Gonzalez, who underwent arthroscopic surgery on his right knee earlier this offseason.

Texas had interest in Oliver but -- as was the case with C.J. Wilson -- never made him a formal offer that was close to being competitive to what the Blue Jays offered.

Oliver, the top southpaw reliever on the market, appeared in 61 games for the Rangers and was 5-5 with a 2.29 ERA, which ranked 11th among American League left-handed relievers with 50 innings pitched.

Over 51 innings, Oliver struck out 44, allowed 47 hits and walked 11. He has appeared in the playoffs six straight seasons with the Mets, Angels and Rangers.

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.