Four people died when a Super Puma L2 helicopter crashed west of Sumburgh Airport at around 18:20 BST.
They were named as Duncan Munro, 46, from Bishop Auckland, Sarah Darnley, 45, from Elgin, Gary McCrossan, 59, from Inverness, and George Allison, 57, from Winchester.
The helicopter was carrying 18 people, with 14 rescued after the aircraft crashed into the sea in foggy conditions.
Three of the bodies have been recovered so far, with one still missing.
The helicopter was carrying two crew and 16 workers from the Borgsten Dolphin oil rig platform to Shetland when it ditched.
Helicopter operator CHC said in a statement that it did not know the cause of the accident but that a "full investigation" would be carried out.
As a precaution, it has temporarily suspended all of its Super Puma L2 flights worldwide.
Commenting last night on the crash, the Moderator of the General Assembly of the Church of Scotland, the Right Reverend Lorna Hood said: "Our thoughts and prayers are with all those involved in the Super Puma helicopter crash off Shetland and especially those waiting news of their loved ones."