Last season, the switch hitter combined his usual Gold Glove calibre defence with a career season at the plate, hitting .313 with 19 homers and 79 RBIs for the Rangers.
"His ability to be a switch-hitter, his versatility and the ability to lead off and to hit in the middle of the order... I think he is a great fit," Angels manager Mike Scioscia told MLB.com.
A later bloomer, Matthews was unwanted for much of his career, having played for the Chicago Cubs, Pittsburgh Pirates, New York Mets, Baltimore Orioles and San Diego twice, before signing with Texas as free agent in 2004 and developing into an all-star.
Trachsel joins Orioles
This off-season, the 32-year-old outfielder had plenty of people knocking at his door before deciding on the Angels and a return to Southern California.
"We approached Gary right from the outset," general manager Bill Stoneman added. "There was a period after he filed for free agency when you couldn't make any offers.
"There was a waiting period, but we made him aware right away that we were interested."
Brewers sign Suppan in record deal
McCarthy joins White Sox