Lowe said Wednesday that he had no hard feelings over Tampa Bay's decision.
"I have a lot of respect for this organization," Lowe said. "The reasons they brought me in here and the way that they treated me, they're a class act."
In parts of eight seasons in the Majors, the 30-year-old Lowe has a 4.17 ERA in 264 games over stints with the Mariners, the Rangers and the Angels. Lowe had a 9.26 ERA in 11 appearances for Los Angeles last season, but he posted a 3.63 ERA with 70 strikeouts against 32 walks in 84 1/3 innings with Texas from 2011-12.
This spring, Lowe allowed just one earned run with 12 strikeouts and one walk in 10 1/3 Grapefruit League innings.
"I've never had a spring go this well," Lowe said Wednesday. "I was throwing a lot of strikes. I had good stuff. And I was using both sides of the plate with all of my pitches. That usually doesn't happen with me during Spring Training, so I came in and did what I had to do."
Cleveland's Opening Day bullpen includes closer John Axford, setup men Cody Allen and Bryan Shaw, lefties Marc Rzepczynski and Josh Outman and right-handers Vinnie Pestano, Blake Wood and Scott Atchison.
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.