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."
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Outbreaks of rain and strengthening winds will affect southernmost parts of England and Wales today.
An earlier debate on the issue was suspended as an 'expression of support' following the Westminster terror attack.
Five people were killed and dozens more were injured after a car and knife attack in the capital on Wednesday afternoon.