Their bodies were recovered from the aircraft shortly after 5pm on Tuesday, a Humberside Police spokesman said.
The helicopter crashed into the sea at Flamborough, East Yorkshire, at around 1.40pm and was witnessed by people playing golf on a nearby course.
A witness had said one body had been recovered from the JetRanger helicopter which came down at high tide at Flamborough, sparking a huge rescue operation.
A spokeswoman for the Air Accidents Investigation Branch said a team had been sent to the scene to investigate.
Video footage released by the RNLI shows one lifeboat crew battling high seas in an attempt to reach the crash site.
The crew from Flamborough RNLI and a second boat from Bridlington were told to abandon the rescue mission and instead search the bay for wreckage.
Flamborough RNLI crew member Cole Ibbotson said: ‘We could see the wreckage of the helicopter at the bottom of the cliff and could see where it had hit.
“The swell was too big for the lifeboat to get in close so we were tasked to undertake a search pattern for wreckage with Bridlington all-weather lifeboat. We recovered a number of items which we have passed on to the police.
‘We are all devastated that this service didn’t have a positive outcome and that we couldn’t help the people on board the helicopter. Our thoughts and sympathy are very much with their family and friends tonight.”
The helicopter had taken off from an airfield near Edinburgh yesterday morning and was due to refuel at Humberside Airport before continuing to its destination near Retford, Nottinghamshire.
Chris Palmer, 33, a builder from Dunswell, East Yorkshire, said he was in shock after seeing the helicopter crash.
He added: “I was with my parents, we all saw the helicopter flying along the coastline, we heard a big crack and saw the helicopter start to descend like a plane and go behind the cliffs.
“By the time I got to the cliffs, there was no sign of it because it had gone under the water. We’re in shock that it’s happened. It’s an absolute tragedy.”
Mr Palmer described the helicopter as white, with no markings, and said he believed it was privately owned.
Earlier a Ministry of Defence spokesman said: “ A search-and-rescue Sea King helicopter from RAF Leconfield was on a training exercise and was very quickly on the scene.
“The tide was high and the Sea King crew were not able to recover anybody from the helicopter before having to return to Leconfield to refuel.
The Sea King has returned to the crash scene.”
The Maritime and Coastguard Agency said: “The Humber Maritime Rescue Coordination Centre received a call at 1.40pm that a small helicopter had gone into the water below the cliff, between the lighthouse and Flamborough Head golf course.
“A coastguard officer was winched down to assess the crash site by the search and rescue helicopter from Leconfield.”
A spokeswoman for Yorkshire Air Ambulance said it also had a crew at the scene and two lifeboats were launched.
Golfers at Flamborough Head Golf Club said they thought the helicopter had been trying to land near the club’s 17th green.
Scott Cooper, assistant greenkeeper, said: “We were on the first green doing some bunker repair work and I glanced across because you hear everything up here.
“I saw a white helicopter which looked to be OK at first, it didn’t seem to be in any trouble.
“Then it started to splutter and it started to sway and I thought the pilot was trying to make a landing but it didn’t make it. We heard a bang and all ran across.
“We couldn’t see a great deal over the cliffs but a few bits of the helicopter and there was a very strong smell of fuel. It was awful.”
Golfer Barry Mills, who was on the course at the time, said: “We heard a clank and it just went down.”
Humberside Police said the crash area had been cordoned off. Members of the public were asked to stay away due to dangerous cliff edges and aviation fuel in the water.
Rod Marwood, 67, the course chairman at the club said he was about 400 yards away when the helicopter crashed.
He said: “There were quite a few members out on the course and we see helicopters flying backwards and forwards all the time. This one was just a small, two to four seater one flying along. I didn’t really take much notice of it when all of a sudden the engine noise changed.
“When I looked, it was already starting to bank a little bit. I thought it was trying to land on the edge of the golf course but it disappeared over the side of the cliffs.
“I didn’t hear anything but I think it hit the cliffs before it went into the sea and then there was a smell of aviation fuel.”
Mr Marwood said the site of the crash was at the bottom of 250-ft high sheer cliffs.
A Humberside Police spokesman said: “Emergency services including the air ambulance, the coast guard and air sea rescue attended the area right away and a search was carried out which resulted in the helicopter being located in the sea off the coast of Flamborough near the light house.
“Two men were recovered from the aircraft shortly before 1700 hours. Both sadly deceased.
“The Air Accidents Investigation Branch will be leading the investigation into the incident to establish the circumstances which resulted in the aircraft crashing into the sea.”
The incident is the latest in a string of UK helicopter crashes.
In January last year, in thick fog over morning rush-hour London, an Agusta 109 helicopter hit a crane in Vauxhall and crashed 700ft to the ground.
Pilot Pete Barnes was killed, as was pedestrian Matthew Wood, while 12 people on the ground were injured, with buildings damaged.
A few months later, in August, four people died when their Super Puma helicopter, carrying 16 passengers and two crew, crashed in the North Sea close to Sumburgh airport in Shetland Islands. It was the latest of a series of North Sea accidents.
On a Friday night in late November, a Eurocopter EC135 helicopter supporting police operations crashed on to the roof of a packed pub - the Clutha Vaults - in central Glasgow.
The pilot, two police officers on board and seven people in the pub were killed.
In January this year, four crew members died when a US military helicopter crashed on a training mission in a nature reserve in Cley-next-the-Sea in Norfolk.
Just a few weeks later - on the evening of March 13 - an Agusta AW139 helicopter crashed in dense fog just after taking off from Gillingham Hall near Beccles in Norfolk.
Two passengers, including Tory peer Lord Ballyedmond, were killed, as were the two pilots.
In March, following a six-week fatal accident inquiry in Scotland, a sheriff principal found that a North Sea helicopter crash that killed 16 men in 2009 could have been avoided.
Fourteen oil workers and two crew died when a Bond Super Puma plunged into the sea off the Aberdeenshire coast on April 1 2009.
Just a few weeks before, on February 18 2009, a Super Puma helicopter ditched in the North Sea but everyone on board survived.
There were two other non-fatal North Sea ditchings in 2012 involving Super Pumas. All 14 people were safely rescued on May 10, while 19 survived in an incident on October 22.