There were no injuries in the ditching and all 19 people on board are being taken by helicopter to Kirkwall in Orkney, the coastguard said.
It is understood the helicopter was flying from Aberdeen to the West Phoenix drilling rig, about 86 miles (140km) north-west of Shetland.
A spokesman for the coastguard said the weather in the area was good.
"It has been quite calm today and that has been favourable in terms of getting the rescue crews to the scene quickly."
More top news
Well-placed sources have reported that Theresa May's deputy will not be forced to step down over allegations of sexual misconduct.
A whistle-blower told ITV News some school buses were on the road without a valid MOT.
It will be the coldest night of the year - freezing with widespread ice.