The Knicks announced on Monday afternoon that they have waived Stoudemire, who signed a five-year, $99.7 million contract with New York in July 2010.
Stoudemire, making $23.4 million this season, is expected to clear waivers on Wednesday at 5 p.m. ET and become a free agent.
"I feel truly blessed to have been able to play for the incredible New York fans, Mr. Dolan, my coaches, teammates and the entire Knicks organization for the past five years," Stoudemire said in a statement released by the team. "I will be forever grateful for the opportunity to contribute positively on the court and in the community.
"Although I leave the Knicks with a heavy heart, I wish the organization the best of luck. Once a Knick always a Knick."
Sources with knowledge of his thinking told ESPN on Monday that Stoudemire is leaning toward signing with the Dallas Mavericks. Another source told ESPNDallas.com that the Los Angeles Clippers and Phoenix Suns also have expressed interest.
Sources also say the Golden State Warriors, Memphis Grizzlies, Portland Trail Blazers and Cleveland Cavaliers -- all playoff contenders in the market for extra size -- are not actively pursuing Stoudemire. The 6-foot-10 center is in his 13th NBA season and has averaged 12.0 points and 6.8 rebounds in 36 games for New York this season.
Stoudemire, 32, has stated a desire to compete for a championship. He posted a farewell message, written in the form of a poem on his Instagram account Monday.
Poem by: Amar'e Stoudemire NY NY what a beautiful city A place where you can hang out with Anna, JayZ & Diddy Its a place absent of excuses and patience If your smart, you can meet leaders of every nation NY NY big city of dreams Everything in NY isnt always what it seems In the land where the jungle is concrete The money flows Dow Jones and Wall Street Home of #STATcity and the #Knickstape Orginator, Shalom to all my fans, Salute to all my haters. Peace and Love Amar'e Carsares Stoudemire Sr.
Knicks president Phil Jackson said Stoudemire initiated the idea of leaving the team. He also praised Stoudemire for his effort over the past five seasons in New York.
"His time here should be marked by recognizing his effort -- it was 100 percent," Jackson said in a statement. "As we move forward in structuring this team, we will look for players that exhibit his desire to win."
Knicks general manager Steve Mills added that he appreciates Stoudemire's contributions.
"Everyone here at the Knicks organization appreciates the contribution Amar'e has made to the team and the entire City of New York over the past five seasons," Mills said. "We have developed a relationship that has translated into a long-term friendship, and it will continue through the remainder of his NBA career, and beyond."
Stoudemire leaves a mixed legacy in New York. The Knicks made the playoffs in Stoudemire's first three seasons but have regressed since.
Stoudemire, a six-time All-Star, has also been hampered by injuries throughout his Knicks tenure.
He missed 70 of the Knicks' 164 regular-season games from 2012-13 and 2013-14, sitting out mostly because of recurring knee issues. He had missed 14 of the previous 18 games this season -- because of ankle, wrist and knee injuries -- before returning in a Feb. 6 loss to the Brooklyn Nets.
The Mavs can offer Stoudemire only the veteran's minimum, but he likely would have a significant role off the bench as a candidate for minutes at power forward and center behind Dirk Nowitzki and Tyson Chandler.
"He would fit in great because we play a lot of pick-and-roll," Chandler, who played with Stoudemire in New York the past three seasons, said recently. "Coach [Rick Carlisle] does an excellent job understanding scorers and how to get them the ball and putting them in a position to succeed. Not only that, we've got the best training staff in the league. That also helps."
By parting ways with Stoudemire, the Knicks open up a roster spot. It is unclear whom they will sign, but some in the organization view Thanasis Antetokounmpo, the younger brother of Giannis Antetokounmpo, as the most NBA-ready prospect on its D-League team.
New York (10-43) may not be finished reshaping its roster this season.
According to sources, the Knicks have discussed moving point guards Pablo Prigioni and Jose Calderon. Veteran forward Andrea Bargnani, according to sources, is a candidate to be waived after Thursday's trade deadline, assuming the Knicks can't move him before that.
ESPN.com's Marc Stein and Tim MacMahon contributed to this report.