The 31-year-old was the 2010 AL Most Valuable Player and led the Texas Rangers to consecutive World Series appearances in 2010 and 2011.
Hamilton has batted .304 in his big league career, and all but 90 games of it in Texas. In 2008, he hit a record 28 home runs in the opening round of the Home Run Derby and finished with 35 home runs, the second-most in Home Run Derby history.
Speaking Thursday after a Rangers' holiday luncheon, Rangers manager Jon Daniels said he had just been informed of the decision by Hamilton's agent, Michael Moye. He said he was disappointed "to some degree ... but it's business, and everybody's got to make their own calls."
Last offseason, the Angels added first baseman Albert Pujols and pitcher C.J. Wilson, but the Angels still disappointed fans and failed to make the playoffs.
Hamilton was considered a risk by some teams because of his history of alcohol and substance abuse, which derailed his career before his surge with the Rangers over the past five seasons.
ESPN and The Associated Press contributed to this report.