The Super Puma came down near a platform in the ETAP field 125 miles east of Aberdeen. The alarm was raised at about 1840 GMT.
Three were rescued by a Bond company helicopter and will be airlifted to Aberdeen Royal Infirmary.
The other 15 are expected to be brought back to Aberdeen by fast rescue vessel.
This vessel is expected to arrive on the mainland on Thursday morning.
The coastguard said there were no serious injuries, but some people had suffered minor injuries, described as walking wounded.
British military spokesman James Lyne, from the RAF base at Kinloss, said the helicopter had landed upright and floated due to flotation bags which inflate when it lands on water.
The passengers escaped into three rubber dinghies equipped with locator beacons, which were detected by satellites enabling rescuers to pinpoint their exact position.
Fl Sgt Lynne said: "It was all very quick. Within a few minutes of the aircraft ditching we had rescue aircraft on route.
"Luckily the crew and passengers were able to get out safely. They were pretty well-equipped.
"The big danger is if it is high seas because then the aircraft will land and turn upside down. They all managed to get out safely. It is a very good result."
He said he could not explain why it had gone down but said an investigation was under way.
People on board the installation, which is operated by BP, saw the incident unfold, and raised the alarm with the coastguard.
There were initial reports of lifejacket lights being seen in the water, and signals being picked up from personal locator beacons, which are attached to lifejackets.
Three flares were also reported to have been seen from the platform, and parts of helicopter fuselage were seen on the surface.
Four helicopters, including three in-field aircraft and a Sea King from RAF Lossiemouth, took part in the rescue. A Nimrod from RAF Kinloss was also scrambled.
Grampian Police said they were currently working with the other emergency services, search and rescue and representatives of BP and Bond to co-ordinate the return of the passengers to Aberdeen.
NHS Grampian said A&E staff at Aberdeen Royal Infirmary were now on full alert and were expecting 18 patients.
A phone line had been set up for families of the passengers and crew on 01224 836 479.
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