AirAsia has confirmed that the debris found in the sea is from its Airbus A320 aircraft, with which air traffic controllers lost contact on Sunday.
As reports came through of at least 40 bodies being found in the Java Sea, AirAsia chief executive Tony Fernandes said he was "absolutely devastated".
The Foreign and Commonwealth Office confirmed that one of the 155 passengers aboard the flight from Surabaya in Indonesia to Singapore was Briton Choi Chi Man.
AirAsia said that the passengers included 17 children and one infant. There were also seven crew members.
Mr Fernandes said: "I am absolutely devastated. This is a very difficult moment for all of us at AirAsia as we await further developments of the search and rescue operations but our first priority now is the well-being of the family members of those on board QZ8501."
AirAsia said: "We regret to inform that the National Search and Rescue Agency Republic of Indonesia (BASARNAS) today confirmed that the debris found earlier today is indeed from QZ8501.
"The debris of the aircraft was found in the Karimata Strait around 110 nautical miles south west from Pangkalan Bun (in Indonesia). There were 155 passengers on board, with 137 adults, 17 children and one infant. Also on board were two pilots, four cabin crew and one engineer."
The airline's statement went on: " At the present time, search and rescue operations are still in progress and further investigation of the debris found at the location is still under way.
"AirAsia Indonesia employees have been sent to the site and will be fully co-operating with BASARNAS, the National Transportation Safety Committee and relevant authorities on the investigation.
AirAsia's chief executive Sunu Widyatmoko said: "We are sorry to be here today under these tragic circumstances. We would like to extend our sincere sympathies to the family and friends of those on board QZ8501
"Our sympathies also go out to the families of our dear colleagues."
Choi Chi Man, thought to have been living in Singapore, is believed to have been travelling with his daughter Zoe on tickets bought on Boxing Day.
Some family members seeing TV pictures of the rescue work in a waiting room at Surabaya airport reportedly screamed and wailed uncontrollably at the sight of debris being found, breaking down in tears while they hugged each other.
One middle-aged man collapsed and had to be carried out on a stretcher
The bodies found so far were spotted by the Indian navy with what appeared to be a life jacket and an emergency exit door.
Crews in dozens of planes, helicopters and ships were taking part in the search, and part of the plane's interior, including an oxygen tank, was taken to the nearest town, Pangkalan Bun, along with a blue plastic suitcase that appeared to be in perfect condition.
First Admiral Sigit Setiayanta, naval aviation centre commander at Surabaya Air Force base, said some bodies were spotted off Borneo island about 10 miles from the plane's last known co-ordinates. The bodies and wreckage were found about 100 miles from land.
Rescue workers were shown on TV being lowered on ropes from a hovering helicopter to retrieve bodies, with their efforts hindered by 6ft waves and strong winds.
What appeared to be more wreckage had been seen under the water, which was clear and a relatively-shallow 65ft to 100ft.
Pilots of the jet had been worried about the weather on Sunday and sought permission to climb above threatening clouds, but were denied due to heavy air traffic. Minutes later, the jet was gone from the radar without issuing a distress signal.
Nearly all the passengers and crew are Indonesians, who are frequent visitors to Singapore, particularly on holidays.
Meanwhile, another AirAsia plane has been involved in a landing in which passengers had to disembark via the emergency slides after an apparent over-shooting of the runway in bad weather at Kalibo on Panay Island in the Philippines.
One passenger, Ms Jet Damazo-Santos, tweeted: "Just landed in Kalibo on an AirAsia flight that overshot runway. Had to deplane using emergency slide.
"Nobody seems to be hurt. Weather was bad. Plane came to a very abrupt stop."
Toulouse-based aircraft company Airbus, whose planes' wings are made in the UK, said: " The company wishes to offer the sincere sympathies of its management and staff to all those who have been affected by the loss of this aircraft.
"In line with international convention, the official investigation into this accident is being led by the Indonesian National Transportation Safety Committee (NTSC), which will be supported by relevant international safety agencies.
"These include the French safety investigation authority BEA, which is an accredited party representing the state of design and manufacture of the aircraft."
Airbus said t he release of all further information related to the progress of the investigation and the publication of findings would be undertaken by the NTSC.
Airbus reaffirmed "its full commitment to provide all necessary technical assistance to the investigation authorities in order to establish the cause of this tragic accident".
The UK's Air Accidents Investigation Branch (AAIB) is helping in the search.
An AAIB spokesman said: "The AAIB is assisting Indonesian authorities in the search for AirAsia QZ 8501 flight recorders.
"An AAIB investigator has arrived in Singapore and has met with Singaporean air accident experts who are assisting the Indonesian investigation. This follows an offer of help by the UK Government to Indonesian and Singaporean authorities which was accepted."