The state governor spoke of a "miracle on the Hudson".
One person suffered two broken legs and paramedics treated 78 patients, most for minor injuries.
Investigators have brought in a giant crane and a barge to help pull the jet out of the river, the Associated Press reports.
Their focus is expected to be on recovering the black box and interviewing the crew about what happened.
Flight 1549 departed LaGuardia en route to Charlotte, North Carolina, at 1526 local time (2026 GMT) on Thursday, after delays, said Laura Brown of the Federal Aviation Administration.
"We believe it was airborne for three minutes after take-off when it crashed into the Hudson River," she said.
The 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, an air controllers union spokesman said.
Ferryboats arrived within minutes of the crash to begin the rescue as passengers emerged in life jackets.
1
1526 local time (2026 GMT): Flight 1549 takes off from LaGuardia airport
2
1527 (2027 GMT): Pilot Chesley Sullenberger reports birds hitting engines
3
1528 (2028 GMT): Pilot told to land at Teterboro airfield
4
1531 (2031 GMT): Pilot ditches plane in Hudson River
The temperature was almost -7C and the current in the Hudson was running rapidly.
The plane moved rapidly down river, threatening to submerge at one point, until guided to a halt by tug boats against a pier.
"It wasn't wild or erratic but if as it was landing on a runway," said eyewitness Stephanie Nachman, who works in a high-rise building in Times Square.
Within minutes, she added, people got out, doors popped out and rafts unfurled.
Jeff Kolodjay, a passenger on the plane, described the moments before the landing:
"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.
BIRD STRIKE DANGER
Large passenger jets can withstand being hit by a 4lb (1.8kg) bird, but problems can arise with flocks of small birds, or with larger birds
219 people have been killed worldwide as a result of wildlife strikes since 1988
In 2007, over 7,600 birds and other wildlife were reported to have hit civil aircraft in the US
Bird strikes cause $600m damage to aircraft in the US every year
"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."
Moments after impact, the situation inside the plane was "just controlled chaos", said passenger Dave Sanderson, of Charlotte.
"People started running up the aisle, people were getting shoved out of the way," he said.
Another passenger, Alberto Panero, said that a couple of people then "just kind of took charge and calmed everyone".
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