West was 5-3 with a 3.34 ERA in 41 appearances (one start) between Double-A Frisco and Triple-A Round Rock last season, striking out 64 batters in 56 2/3 innings.
Burns, 27, was claimed off waivers in September from the Rays.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.