Morales had played his entire six-year career for the Angels, racking up a .281 average with 79 home runs and 265 RBI.
He missed most of 2010 and the entire 2011 season with a broken leg when he was injured during a home plate celebration after belting a game-winning grand slam in a May 29, 2010 contest.
He rebounded this past season, hitting .273 with 26 doubles, 22 home runs and 73 RBI in 134 games for the Angels.
The left-handed Vargas, meanwhile, was one of the Mariners' most reliable starters in 2012, compiling a 14-11 mark with a 3.85 ERA and 141 strikeouts in 33 starts for Seattle.
The seven-year veteran has posted a 42-50 record with a 4.35 ERA during stints with Florida, the New York Mets and Mariners.
Celebrity Families of 2014 [PHOTOS]