Haren, a three-time All-Star from 2007-09, gets a $3.5 million buyout under the deal, which included a $15.5 million club option for 2013. The Angels' decision came after a proposed trade to the Chicago Cubs for closer Carlos Marmol fell apart.
Los Angeles also declined to make a $13.3 million qualifying offer to free-agent outfielder Torii Hunter.
"We want to create as much flexibility as we can in our ability to navigate for 2013 and beyond," general manager Jerry Dipoto said. "In business, sometimes you make tough decisions."
The Angels agreed to trade Haren to the Cubs, a person familiar with the negotiations told
Marmol's contract gives him the right to submit a list of up to five teams he can't be traded to without his consent. The person said Marmol told the Cubs he would agree to the trade, but would not say whether the reliever provided his written consent.
A spokesman for the Cubs declined to comment.
"Obviously, it didn't happen," Dipoto said. "We had a variety of different deals that we worked through during the course of the last week or 10 days. Some were closer than others. But I'll leave it at that."
Marmol, an All-Star in 2008, had 114 saves for the Cubs over the past five years. Yet he lost his job as the team's closer several times due to ineffectiveness and a lack of control.
The Angels had until midnight EDT on Friday to exercise Haren's option for next season. The 32-year-old right-hander went 12-13 with a career-worst 4.33 ERA in 30 starts this year and was on the disabled list for the first time.
Haren became the second starting pitcher in three days to be jettisoned by the busy Angels. They shipped Ervin Santana to the Kansas City Royals on Wednesday for minor league left-hander Brandon Sisk.
In addition, Zack Greinke became a free agent.
"Obviously, we have a great interest in Zack Greinke. We traded for him once. He did a tremendous job for us in the second half of the season and down the stretch, and we have a great deal of interest in pursuing the potential of bringing him back," Dipoto said. "But there is a lot that has to happen between now and opening day next year that will define whether that's going to happen or not."
"You can't just continually gather assets without having logical solutions as to how they all fit," Dipoto said.