Guilmet, 26, was drafted by Cleveland in the ninth round of the 2009 First-Year Player Draft, and he posted a 1.68 ERA with 20 saves in 49 games for Triple-A Columbus in 2013.
"[He] has command of his fastball, slider and split-finger, which he mixes to get hitters out," O's executive vice president Dan Duquette said of Guilmet in a text message. "We expect he'll contribute to the [Major League] team this season given his track record and experience closing games."
Last season in Columbus, Guilmet averaged 10.1 strikeouts per nine innings and appeared in four games for the Indians, posting a 10.13 ERA in 5 1/3 innings.
Brittany Ghiroli is a reporter for MLB.com. Read her blog, Britt's Bird Watch, and follow her on Facebook and Twitter @britt_ghiroli. This story was not subject to the approval of Major League Baseball or its clubs.