Alvarez signed a minor-league contract with the Twins on Thursday, Brandon Warne of ZoneCoverage.com reports.
The southpaw spent much of last season with the Mariners' Triple-A affiliate, producing a 1.98 ERA, a 1.25 WHIP and a 28:14 K:BB in 27 frames. He was released in early August, though, allowing him to test the free agent market this offseason. Alvarez will join the Twins organization looking for a big-league bullpen spot, though there are already a few lefties at the major-league level who could force Alvarez to spend even more time in the minors.