A product of Venezuela, Sulbaran spent last season with Class A Great Lakes and Cedar Rapids, going 9-4 with a 2.96 ERA in 27 games (20 starts). In 112 2/3 innings, Sulbaran allowed 110 hits and 32 walks, recording 101 strikeouts.
Nunez, 26, was designated for assignment when the Yankees chose to take Dean Anna and Yangervis Solarte as the backup infielders on their Opening Day roster. In 270 career games with the Yankees, Nunez hit .267 with 10 home runs, 76 RBIs and 48 stolen bases.
The Twins have said that Nunez will be assigned to Triple-A Rochester.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.