Avila hit .207 with nine home runs and 24 RBIs in 63 games for the Arizona Diamondbacks last season. He also pitched in two games.
Avila, who turns 33 in January, has a career .235 batting average with 103 homers in an 11-season career with Detroit, the White Sox, the Cubs and Arizona.
The AL Central champion Twins had been looking for a reliable backup this offseason. Jason Castro became a free agent, so Minnesota was in the market for a veteran complement to Mitch Garver after his breakout season in which he hit 31 home runs in 93 games.
The Associated Press contributed to this report.