Mathis has spent his entire career with the Angels, who selected him in the first round of the 2001 draft. Mathis broke into the majors in 2005 and has appeared in 426 games, hitting .194 with 26 home runs and 139 runs batted in.
The 28-year-old played in 93 games last season, hitting .174.
Mills was a fourth-round pick in the 2007 draft by Toronto, but has spent most of his career in the minors.
He has pitched in 14 games (nine starts) for the Blue Jays between 2009-11, posting an 8.57 earned run average in 48 1/3 innings.
Last season for Triple-A Las Vegas, Mills posted an 11-9 record and 4.00 ERA in 24 starts.