Rodriguez's decision, announced by agent Scott Boras as the rival Boston Red Sox completed their World Series sweep of Colorado, makes the third baseman eligible to become a free agent.
Boras said he attempted to notify Yankees general manager Brian Cashman of the decision but couldn't reach him, so he left a voice mail.
''He was traveling and I was traveling,'' Boras said.
Rodriguez loses the final $72 million in guaranteed salary in the record contract, which he signed with Texas before the 2001 season. The Yankees lose $21.3 million in remaining payments from the Rangers, a subsidy agreed to at the time of his 2004 trade. New York has 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. Boras said it became clear that the others wouldn't make a decision by Rodriguez's deadline to opt out - 10 days after the World Series.
''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.''
Cashman did not respond to messages seeking comment.
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.
A Yankees official and an agent who deals regularly with the team said it appears Cashman was leaning toward recommending Girardi.
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 are still 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 majors with 54 homers and 156 RBI. He was announced as a winner of a Hank Aaron award for offensive achievement before Game 4 but wasn't on hand to receive it. Boras said Rodriguez had a family commitment.
New York was preparing to offer Rodriguez a four- or five-year extension worth between $25 million and $30 million annually.