Ogando has dealt with right shoulder and elbow issues over the past few seasons. He made just 27 appearances and posted a 6.84 ERA for Texas last season because of elbow inflammation, and he endured shoulder and biceps issues in 2013.
To make room for Ogando on the 40-man roster, left-handed pitcher Drake Britton was designated for assignment.
Adding Ogando is just one of many moves the Red Sox have made this offseason to retool their bullpen. Boston acquired Anthony Varvaro via trade with the Braves and Robbie Ross Jr. earlier this week in a deal with the Rangers. The Red Sox also signed former Cardinals reliever Mitchell Boggs to a Minor League deal with an invitation to Spring Training.
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.