The 30-year-old right-hander has spent most of his career with Oakland. He has a 12-6 career record with one save and a 3.46 ERA in 158 relief outings.
To make room on the 40-man roster, the Indians designated outfielder Jerry Sands for assignment.
Otero spent most of last season with the Athletics, allowing two runs over his final seven appearances. The Phillies claimed him off waivers on Nov. 3.
He has shown remarkable control during his career, averaging 1.41 walks per nine innings and allowing 11 home runs in 184 2/3 innings. In 2014, he went 8-2 and pitched 86 2/3 innings.
Cleveland is awaiting medical tests on first baseman Mike Napoli, who agreed to a one-year, $7 million contract this week.