Agent Happy Walters said the five-time All-Star made the move Wednesday after talks with Suns owner Robert Sarver failed to result in an agreement on a contract extension. The last year of Stoudemire's contract was worth about $17.7 million.
"I opted out of my contract with PHX," Stoudemire said on his Twitter account. "Can't wait to see what lies ahead. I had a blast with my teammates last season. What's Next!!"
Walters said the Suns remain in the picture but the 6-foot-10, 249-pound power forward wants to see what develops on the free agent market. Stoudemire has been with the Suns since he was drafted out of high school, as the ninth pick overall, in 2002.
Walters said he and Stoudemire met for three hours with Sarver and Suns coach Alvin Gentry in Los Angeles on Tuesday night.
"The Suns have been great and Amare loves them," Walters said. "It's just trying to make both sides comfortable and happy with everything."
Stoudemire wants a contract with the maximum money and length the NBA allows but Walters said "if it all worked out, he might take less to stay in Phoenix than he would elsewhere."
The Suns reportedly didn't want a six-year deal, the longest allowed under league rules, because of concerns over Stoudemire's health. He missed all but three games of the 2005-06 season to undergo and recover from microfracture knee surgery. He was sidelined the final 29 games of the 2008-09 season after surgery to repair a partially detached retina.
Walters said he expected to start hearing from teams interested in Stoudemire shortly after the free agency period began at midnight EDT. That's 9 p.m. Los Angeles and Arizona time.
The Suns conducted the last stages of their negotiations without a general manager after Steve Kerr stepped down. Kerr's contract expired Wednesday and he did not take part in the Tuesday talks.
Stoudemire, nicknamed "Stat" by his teammates, teamed with Steve Nash to form one of the NBA's most formidable pick-and-roll combinations. He played in every game last season, averaging 23.1 points and 8.9 rebounds. He averaged 22.2 points in Phoenix's surprising playoff run to the Western Conference finals, but his rebounds dropped to 6.6 per game, just 5.5 in the conference finals against the Los Angeles Lakers.
Stoudemire has career averages of 21.4 points and 8.9 rebounds.