Rodriguez's decision, announced by agent Scott Boras during Game 4 of the World Series, makes him eligible to become a free agent.
Rodriguez loses the final $72 million in guaranteed salary in the contract, of which $21.3 million was to be covered by payments from the Texas Rangers to the Yankees, and becomes eligible for free agency. New York had said it would not attempt to re-sign A-Rod if he opted out.
Boras said during a telephone interview that Rodriguez made his choice because he was uncertain whether Mariano Rivera, Jorge Posada and Andy Pettitte would return to the Yankees.
"Alex's decision was one based on not knowing what his closer, his catcher and one of his statured pitchers was going to do," Boras said. "He really didn't want to make any decisions until he knew what they were doing."
Boras said he attempted to notify Yankees general manager Brian Cashman of the decision Sunday but couldn't reach him, so he left a voice mail.
"He was traveling and I was traveling," Boras said.
A-Rod, likely to win his third AL MVP award next month, made his decision before the Yankees announced a replacement for departed manager Joe Torre. Broadcaster Joe Girardi and bench coach Don Mattingly were the top contenders, and the team also interviewed first-base coach Tony Pena.
Texas turns out to be the biggest winner, saving the remaining money it would have had to pay New York as part of the 2004 trade. Boras said the Rangers remain responsible for $3 million in annual deferred money A-Rod is owed in the next three years under the contract.
"We're going to wait until we hear officially, but obviously it would be welcome news on our end," Rangers general manager Jon Daniels said in an e-mail to The Associated Press.
Rodriguez hit .314 this year and led the major leagues in home runs and RBIs. He was announced as a winner of a Hank Aaron award for offensive achievement before Game 4 but was not on hand to receive it. Boras said Rodriguez had a family commitment.
By Ronald Blum and Stephen Hawkins