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
The former prime minister made the comments as he prepares to return to politics saying he wants to be "part of the debate" on Brexit.
The new measures would mirror childcare vouchers and see workers sacrifice some of their salary to benefit.
Google, Facebook and Twitter could face multi-million pound fines over their failure to remove illegal content, MPs say.