Rescue boats plucked passengers, who could be seen wearing life jackets, from the wings of the plane.
The BBC's Greg Wood, in New York, says the aircraft was drifting rapidly down the Hudson as the rescue was carried out.
Our correspondent says there is a mood of overwhelming relief in New York that there was no loss of life.
US Airways gave an emergency number for people who believe they may have had relatives on the flight: 1-800-679-8215.
'Like on a runway'
Flight 1549 departed LaGuardia at 1503 local time (2003 GMT), after a delay of 18 minutes, the airline said.
BBC News website reader Nigel Baker took this picture of the plane
According to an air controllers union spokesman, a US Airways pilot reported a "double bird strike" less than a minute after take-off and asked to return to the ground, before ditching in the Hudson.
The spokesman, Doug Church, said the pilot apparently meant that birds had hit both of the plane's jet engines. It appears the birds involved were a flock of geese.
Stephanie Nachman, who works in a high-rise building in Times Square, told the BBC she had seen the plane crash.
She said she had seen the plane flying very low over the Hudson and was shocked by how low.
Then it landed in the water, she added, but "it wasn't wild or erratic but if as it was landing on a runway".
Within minutes, she added, people got out, doors popped out and rafts unfurled.
Eyewitness accounts of NY crash
Jeff Kolodjay, a passenger on the plane, described the crash for the BBC.
"About three or four minutes into the flight... the left engine just blew... flames coming out of it and I was looking right at it cos I was sitting right there.
"And it just started smelling a lot like gasoline and a couple of minutes after that the pilot said 'you guys gotta brace for a hard impact'.
"And that's when everyone started, to be honest, saying prayers and we looked over the water and we thought we had a chance because, you know, there's some water.
Asked how he got out of the plane he said: "At first chaos, but everyone was kind of orderly, man. You know after a while everyone, we just, I just kept saying relax relax, women and children first. And then it just started filling with water, quick."
New York Mayor Michael Bloomberg said that police divers had rescued some people from the water.
A spokesman at St Luke's Roosevelt hospital in Manhattan told Reuters that he expected as many as 50 patients with exposure and secondary injuries, while people with more serious injuries were being sent to nearby hospitals.
New York Senator Charles Schumer said it was a modern-day miracle that no one had been killed.
"The pilot was truly heroic - that's the preliminary indication," he said.
"He saw what was happening, gained a low altitude, turned the plane in the right direction, found the Hudson River and made sure it wasn't a nose-first landing but rather flat.
"And that's probably what saved everybody's life, thank God."
"Gotta give it to the pilot, man, he made a hell of a landing," said passenger Jeff Kolodjay.
America's National Transportation Safety Board has announced it is is sending a team to investigate the crash.
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