The Angels also didn't offer deals to reliever Juan Gutierrez and third baseman Chris Nelson.
With a projected 2014 payroll nearing the luxury-tax threshold of $189 million, the Angels' decisions likely saved them roughly $10 million, possibly enough to add starting pitching to a thin rotation.
Los Angeles tendered contracts to five arbitration-eligible players: designated hitter Mark Trumbo, new third baseman David Freese, closer Ernesto Frieri, and relievers Kevin Jepsen and Fernando Salas.
The Angels decided to part ways with Williams, who revitalized his career with the club in 2011 after three years out of the majors. The right-hander went 19-18 in 79 appearances with Los Angeles, making 25 starts this past season while serving as a dependable arm on a disappointing pitching staff.
"I wanna thank the Angels organization for the opportunity to get back in the big leagues," Williams posted on his Twitter account. "It's been an awesome time. Met new faces and even better people. Wish all the guys luck in the next upcoming year. Now it's time to move on to the next chapter."
The Angels' starting pitching struggled for most of this past season, their fourth straight out of the playoffs. Their returning starters are Jered Weaver, C.J. Wilson and Garrett Richards after they were outbid last month for left-hander Jason Vargas, who got a four-year, $32 million deal in Kansas City.
Hanson flopped in his only season back in his native Southern California, going 4-3 with a 5.42 ERA and a demotion to the minors. Los Angeles acquired him from Atlanta for reliever Jordan Walden last winter.
The Angels also have right-hander Joe Blanton under contract for $7.5 million next season despite his dismal debut with the club, going 2-14 with a 6.04 ERA and a midseason ouster from the rotation.
Nelson was the Angels' starting third baseman in August but missed the rest of his only season in Anaheim with an injured hamstring. Freese will be Los Angeles' third baseman after arriving last month in a trade with St. Louis.