Burns was designated for assignment by the Padres on Nov. 20, meaning the team had 10 days to either trade, release or place him on waivers for the intention of giving him his outright release.
Burns, 25, appeared in 17 games last season, compiling a 5.50 ERA in 18 innings with 18 strikeouts and 10 walks. He spent the majority of the season with Triple-A Tucson, going 1-2 with a 3.14 ERA over 54 appearances with 78 strikeouts in 66 innings.
The Padres obtained Burns last December, sending outfielder Aaron Cunningham to the Indians. Over parts of four Minor League seasons with the Indians and Padres, Burns is 7-11 with a 2.36 ERA.
Also on Wednesday, the Padres announced the signings of four players to Minor League contracts with Spring Training invitations -- outfielder Travis Buck, right-handed pitchers Daniel Stange and Jason Ray and catcher Eddy Rodriguez.
The 29-year-old Buck is a career .243/.316/.399 hitter over 910 Major League plate appearances with the A's, Indians and Astros. He's a career .303/.383/.462 hitter in the Minor Leagues. Buck played for Tucson manager Pat Murphy when he was at Arizona State (2003-05).
Stange, 26, was 4-6 with a 4.09 ERA last season in four Minor League stops, two in the Padres' Minor League system. Ray, 28, had a 1-3 record and a 3.57 ERA in 40 games with Tucson.
Rodriguez, 26, hit .217 with 14 home runs and 42 RBIs in two Minor League stops in the Padres' system last season and made his Major League debut on Aug. 2. He hit a home run in his first at-bat against the Reds that day.