Crawford announced his choice on Twitter, posting "Rip city!!!"
The Blazers made it official a few hours later on Thursday when they announced they had signed Crawford. The deal is for two years and $10 million, with a player option for his second year, sources told ESPN The Magazine's Chris Broussard.
"We were a long shot to start with," Knicks coach Mike D'Antoni said on Thursday afternoon, acknowledging the Knicks' low bid for Crawford. "I think the relationships that he had here in New York and how he loved it -- I thought we had a shot at it."
In order to make a deal with Crawford, the team used the NBA's new amnesty clause to waive All-Star guard Brandon Roy, who announced his retirement last week because of ongoing knee problems.
An 11-year veteran, Crawford played for the Atlanta Hawks the last two seasons. For his career, the 31-year-old has averaged 15.2 points, 2.6 rebounds and 3.9 assists. He won the NBA's Sixth Man award in 2010.
"We've thought highly of Jamal for a long time and think he's a great fit for our team," said Chad Buchanan, Portland's acting general manager. "He brings a scorer's touch and veteran leadership that will help us immediately."
Blazers guard Wesley Matthews said he spoke to Crawford on Wednesday night.
"I'm excited about it," Matthews said. "He wants to come and win and that's what we're about."
Crawford, a 6-foot-5 shooting guard, will help the Blazers deal with the absence of Roy and former Blazer Rudy Fernandez, who was traded away on draft night in June.
Matthews said he was unconcerned about potential competition for playing time.
"We can coexist at the same time, similar to what they did in Atlanta with Joe Johnson and him," Matthews said.
By using the amnesty clause to waive Roy, the Blazers freed up salary cap space that allowed the team to use a mid-level exception on Crawford. Roy, who was under a max contract, was set to make $15 million this year.
"Brandon's announcement that he is leaving the game ultimately shifted our decision to amnesty," Buchanan said in a statement. "We're given the immediate option to obtain additional salary cap flexibility as we will no longer be in the luxury tax -- something that is critical to improving our team and helping us recover from the loss of a player of Brandon's caliber."
A three-time All-Star who has played all five of his NBA seasons in Portland, Roy had been dogged by pain for the past two years because he lacks cartilage between the bones in his knees.
He sat for stretches of last season because of soreness and had arthroscopic surgery on both knees last January. He returned to end the season with a career-low average of 12.2 points in 47 games.
Roy, a fan favorite whom many credit with turning around the team's once-tarnished "Jail Blazers" reputation, finished his career with averages of 19 points, 4.7 assists and 4.3 rebounds.
Coach Nate McMillan praised Roy and his proclivity for late-game heroics after practice on Thursday.
"The closer. That's how I look at him," McMillan said. "The closer has closed."
Crawford is close to Roy, a fellow Seattle native.
Buchanan told reporters Thursday afternoon that Roy will always have a place in the organization.
"If there's any role that he wanted to take on moving forward, we would love to have him in any capacity ... there's always going to be a place for Brandon in this organization," Buchanan said. "And at some point he'll probably consider and look into all of his options and what he wants to do now that he's done playing. We just want to make sure that he knows he always has a home with us."
The Blazers also announced that forward LaMarcus Aldridge had been cleared to return to non-contact practice starting on Saturday.
Aldridge underwent a procedure last Friday to treat for Wolff-Parkinson-White Syndrome, a condition which causes the ventricles of the heart to contract prematurely.
Aldridge was diagnosed with the disorder in 2007. He had a similar procedure at the time, and missed the final nine games of the 2006-07 season.
The 6-foot-11 forward from Texas averaged 21.8 points and 8.8 rebounds last season, the best of his five-year NBA career. He had 36 double-doubles.
Portland also signed free agent forward Craig Smith.
Nicknamed "The Rhino," Smith played the last two seasons with the Los Angeles Clippers, averaging 5.4 points and 2.4 rebounds in 48 games.
Terms of the deal reached Thursday were not disclosed. Smith, a five-year veteran, has also played for Minnesota.
Information from ESPN The Magazine's Chris Broussard, ESPNNewYork.com's Ian Begley and The Associated Press was used in this report.