Everyone on board was accounted for and alive, officials said. About 15 people were being treated at hospitals and others were being evaluated at triage centers.
Flight 1549, headed to Charlotte, North Carolina, was airborne less than three minutes, according to FAA spokeswoman Laura Brown.
The pilot radioed to air traffic controllers that he had experienced a bird strike and declared an emergency, a New Jersey State Police source said.
"I think a lot of people started praying and just collecting themselves," said passenger Fred Berretta. "It was quite stunning."
He said he was expecting the plane to flip over and break apart, but it did not.
"It was a great landing," Berretta said.
Air traffic controllers at LaGuardia saw the plane clear the George Washington Bridge by less than 900 feet before gliding into the water about 3:31 p.m., an aviation source told CNN.
Witness Ben Vonklemperer said he watched the plane from the 25th floor of an office building.
"If someone's going to land a plane in the water, this seemed the best possible way to do it," Vonklemperer said. "The way they hit it was very gradual. A very slow contact with the water."
As the situation began to settle Thursday evening, the flight's pilot, Chesley B. "Sully" Sullenberger, emerged as a hero, with praise being heaped on him by passengers, officials and aviation experts.
"I don't think there's enough praise to go around for someone who does something like this. This is something you really can't prepare for," said former Delta pilot Denny Walsh. "You really don't practice water landings in commercial airplanes. Just the sheer expertise he demonstrated is amazing."
US Airways CEO Doug Parker said it would be premature to speculate about the cause of the accident until the National Transportation Safety Board, which is sending a team to the site, completed an investigation.
A source familiar with the situation, however, told CNN the pilot reported a double bird strike, but it was unclear whether that meant birds in both engines or two birds in one engine.
The pilot initially said he needed to go back, and air traffic controllers started to give him clearance to do so, but the pilot said he wanted to head to Teterboro, New Jersey, because it was closer. That was the last transmission from the pilot, the source said.
Passenger Alberto Panero said that within a few minutes after takeoff, he heard a loud bang and smelled smoke.
"That's when we knew we were going down and into the water. We just hit, and somehow the plane stayed afloat and we were able to get on the raft. It's just incredible right now that everybody's still alive."
Passenger Jeff Kolodjay of Norwalk, Connecticut, said he was sitting in seat 22A, near one of the engines.
"The captain came on and said, 'Look, we're going down. Brace for impact.' Everyone looked at each other and we said our prayers. I said about five Hail Marys," said Kolodjay, who was headed to Charlotte to play golf.
"The plane started filling with water pretty quick," he said. "It was scary. There was a lady with her baby on my left-hand shoulder, and she was crawling over the seats."
Police, fire and Coast Guard boats, along with commercial ferries, were quickly on the scene as passengers lined up on slightly submerged safety chutes.
New York Mayor Michael Bloomberg said later Thursday that the plane was tied to a pier at Battery Park City in lower Manhattan. As night fell, Coast Guard and FDNY boats remained at the scene.
President Bush commended those involved in the rescue. "Laura and I are inspired by the skill and heroism of the flight crew as well as the dedication and selflessness of the emergency responders and volunteers who rescued passengers from the icy waters of the Hudson," he said.
Bloomberg also commended the pilot for not leaving the plane until he had checked to make sure everyone had been been evacuated.
"It would appear that the pilot did a masterful job of landing the plane in the river and then making sure that everybody got out," Bloomberg said.
"I had a long conversation with the pilot," Bloomberg said. "He walked the plane twice after everybody else was off, and tried to verify that there was nobody else on board, and assures us there were not."
"There is a heroic pilot," said Gov. David Paterson. "We have had a miracle on 34th Street, I believe we now have a miracle on the Hudson."
The temperature in New York was 20 degrees about the time of the crash off Manhattan's west side.
Dr. Gabriel Wilson, associated medical director of the emergency room at Roosevelt Hospital, said 55 survivors were checked out and cleared to leave from the scene.
Those being treated at hospitals included a husband and wife with hypothermia at Roosevelt Hospital, as well as a flight attendant with a leg fracture, hospital spokeswoman Michelle Stiles said.
Since 1975, five large jetliners have had major accidents in which bird strikes played a role, according to the Web site of Bird Strike Committee USA, a volunteer group dedicated to reducing the frequency and severity of the strikes.
More than 56,000 bird strikes were reported to the FAA from 1998 to 2004, according to the group's Web site.
People who believe they may have had relatives on the flight may call US Airways at 1-800-679-8215 within the United States, the airline said.