Sarah Darnley, 45, from Elgin; Duncan Munro, 46, from Bishop Auckland; 59-year-old Gary McCrossan, from Inverness and George Allison, 57, from Winchester died following the incident yesterday evening.
The aircraft was carrying 16 workers and two crew members at the time of the incident, in which it was believed to have experienced a "catastrophic" loss of power.
Fourteen people were taken to safety during the immediate rescue response.
Police Scotland confirmed that the bodies of three people have been recovered and work is under way to recover the body of the fourth person.
Fourteen people were taken to the Gilbert Bain Hospital in Lerwick, Shetland, for treatment, including the two crew members, officers said.
Five were discharged and nine detained overnight for observation or because they were suffering from exposure.
Assistant Chief Constable Malcolm Graham said: "Our sympathies are very much with the families of those affected at this difficult time. All families have been informed and specially-trained family liaison officers are currently providing them with support.
"This incident has resulted in a large-scale response from a number of different agencies who have worked closely together to deliver a swift rescue operation.
"We have been able to deploy a number of officers with specialist disciplines from across Police Scotland to assist with the operation.
"We will now be carrying out an investigation to establish the circumstances in due course."
The helicopter's operator CHC, has said it was flying for oil company Total and that the aircraft lost communication as it approached the airport on the southern tip of Shetland's main island.
The company said it would co-operate fully with investigations.
Mark Abbey, regional director of the western North Sea for CHC Helicopter, expressed "heartfelt sympathies" to all those involved in the crash.
In a statement, he said: "Following the incident, flights in Aberdeen have been suspended today as a mark of respect for the events of yesterday. Globally, we have temporarily suspended operations of all AS332L2 aircraft until more information is available.
"CHC will not enter into any speculation as to what caused the incident but rest assured a full investigation will be carried out in which we will co-operate fully with all the regulatory bodies and share any learnings with the industry.
"We are proud of our partnership with the industry and, like all helicopter operators, we have advanced considerably in terms of technology and predictability and the safe-guards we put in place to mitigate risk. However in a tragedy like this none of that matters.
"What does matter is that while it is not possible to take all of the risk out of this industry it is our obligation to mitigate those risks and be as safe as we possibly can be."
The naming of the four who died came after a major search operation, involving the coastguard, police, RAF and RNLI, took place overnight for those who were missing.
Jim Nicholson, RNLI rescue co-ordinator, said he understood two of the bodies were recovered in the area where the helicopter crashed.
''The bodies came to the surface close to the helicopter wreckage,'' he said.
''The helicopter was in a pretty inaccessible place but the lifeboat crew were able to get to them using an inflatable craft."
He went on: ''There appears to have been a catastrophic loss of power which meant the helicopter suddenly dropped into the sea without any opportunity to make a controlled landing.''
Pat Rafferty, Scottish secretary of the Unite union, said the number of incidents involving Super Puma helicopters in the offshore industry in recent years was "unacceptable".
He said: "No-one should ever go to work and not come back safely to their family and friends. This is an absolute tragedy.
''This is the fifth major incident in the last four years involving Super Puma helicopters in the UK offshore industry and the second resulting in fatalities. It's unacceptable and it can't go on.
''A full investigation must now take place and the industry's helicopter operators must use every means at their disposal to demonstrate that its fleet is fit for purpose.''
The coastguard previously believed 15 people had been rescued in the aftermath of the incident, but that figure was revised to 14 today.
During the multi-agency operation, rescuers managed to move the helicopter to a more accessible position where it could be searched for missing people.
One of the men rescued, Sam Smith, described how the helicopter suddenly lost power and there was ''no time to brace'', it has been reported.
His mother Amanda Smith told Sky News: ''He said (the helicopter) seemed to lose power and there was no time to brace - they just dropped into the sea.
''He was by the window so he was able to escape that way as it rolled over."
First Minister Alex Salmond said his thoughts were with the relatives of those who died.
He said: ''Our thoughts at this difficult time are with the families, friends and colleagues of those who lost their lives in this tragic incident. We also hope that those who were injured can make a full and speedy recovery.
''I would like to pay a massive tribute to all of those brave and hard-working individuals involved in the rescue effort and in treating the casualties when they were brought ashore.
''It is still too early to know what caused this terrible tragedy, but a full investigation by the relevant authorities is already under way."
Scottish Secretary Michael Moore also said his thoughts were with the family and friends of those who lost their lives and were injured.
He said: "There have been too many reminders in recent years of the dangers involved in our offshore oil and gas industry. The bravery and dedication of those in the industry is never taken for granted and we owe them a debt of gratitude.
"We must find out what caused this tragic accident and an investigation is now underway."
Mr Allison had been working at the Offshore Dunbar Platform as a project safety supervisor for just over a year when he was killed, according to his LinkedIn profile.
He was overseeing conversion work at the platform and at a drilling support vessel, it said.
Describing himself as a "highly qualified, experienced and competent Safety Advisor who has been working in an offshore environment globally for the past 27 years", he said he was highly motivated, hard working and creative.
He listed his interests as swimming, fishing, art, riding his bicycle, cooking and reading.
Bob Crow, general secretary of offshore union RMT, said he expected an "outpouring of anger" in response to the latest incident.
"Workforce confidence in the Super Puma type aircraft was severely dented after the two ditching events of last year and the fatal accident in 2009," he said.
"RMT and Unite have worked with all sectors of the industry to address the concerns of our members and rebuild that confidence. Last nights events have undone all of that work and we anticipate an outpouring of anger."
He went on: "The entire Super Puma fleet must remain grounded until the causes of this latest event are established and dealt with thoroughly to the unions' satisfaction and we will support any member who refuses to board any suspect aircraft type in light of this disaster.
"RMT also demands the lifting of the ban on union access to the offshore workforce which in an infringement of basic rights and makes a mockery of pledges on offshore worker safety."
The UK Air Accidents Investigation Branch (AAIB) confirmed the aircraft involved was a Eurocopter AS332L2 Super Puma.
A team of AAIB investigators is being sent to Aberdeen to carry out initial inquiries into the incident.
A spokeswoman said: "In exercise of his powers, the Chief Inspector of the Air Accidents Investigation Branch (AAIB) has ordered that an investigation into the accident be carried out in accordance with the Civil Aviation (Investigation of Air Accidents and Incidents) Regulations 1996.
"The sole objective of the investigation shall be to determine the cause(s) of the accident with the intention of preventing a recurrence. It shall not be the purpose to apportion blame or liability.
"In accordance with international standards and recommended practices, representatives from the state of design and manufacture of the helicopter and the European Aviation Safety Agency have been invited to participate in the investigation.
"A team of AAIB Investigators is being deploying to Aberdeen to conduct preliminary inquiries to establish the facts surrounding the accident."
In Aberdeen later, the Town House (council headquarters') flag will be flown at half mast as a mark of respect.
Lord Provost of Aberdeen, George Adam, said: "Everyone in this city knows someone who works offshore and so this tragedy hits home with us all.
"It is easy to take for granted the fuel that powers our everyday lives, but we cannot forget the enormous gratitude we owe to these friends, relatives and colleagues who work in such a challenging environment.
"We have a close knit community here, and I know that the heartfelt sympathies of the whole city go out to everyone affected."
The Moderator of the General Assembly of the Church of Scotland, the Right Reverend Lorna Hood, said: "We offer our deepest sympathy and heartfelt sorrow as we pray for all those grieving loss this morning.
"We also offer our gratitude for the bravery of all those involved in the rescue and are reminded once again of the perilous nature of work in the oil and gas industry.
"I will be in touch with our Chaplain to the Oil and Gas Industry the Rev Gordon Craig. I am sure he will be offering his help and support in the aftermath of this incident."
Oil company Total said the four people killed were from contractor organisations.
In a statement, the firm said: "Further to the CHC operated Super Puma L2 helicopter crash in the UK North Sea near Shetland at 6.20pm on Friday evening, in which four people from contractor organisations are confirmed to have been killed, Total E&P UK would like to offer sincere condolences to the families of those who tragically lost their lives.
"Our thoughts are also with the 12 other passengers and two air crew who were also on board the flight, and their families. One Total E&P UK employee was among the passengers and the others represented 12 separate contractor organisations."
All necessary resources have been made available to provide support and assistance to those who were on board the flight, and their families, the statement added.
Mr McCrossan worked for Stork Technical Services who offered their condolences to his family.
Mike Mann, a senior vice president at the firm, said: "Our heartfelt condolences go out to Gary's family and to all of those affected by this tragedy. We are doing all we can to assist the family at this difficult time.
"Stork would like to thank the emergency services for their response and support."
Relatives of Ms Darnley and Mr Munro said the families did not wish to comment.