The UK as a whole has voted to leave the EU by 52% to 48%.
But Scotland returned a Remain majority with all 32 council areas backing to stay in.
In the Western Isles, 8,232 islanders voted to stay while 6,671 people wished to leave.
The islands' outcome works out at 55% -
A second Scottish independence referendum is being proposed.
First minister, Nicola Sturgeon, said the "people of Scotland see their future as part of the European Union" which is being denied by a Brexit vote.
She said an indy vote is back "on the table."
She added: "We will begin to prepare the legislation that would be required in order for a new independence referendum to take place if and when parliament so decides."
David Cameron is to quit as prime minister after his decision to call a referendum backfired.
Mr Cameron, who campaigned for a Remain vote, said: "The British people have made a very clear decision to take a different path and as such I think the country requires fresh leadership to take it in this direction."
He added: "I do not think it would be right for me to try to be the captain that steers our country to its next destination."
Britain votes to leave EU, Scotland backs Remain
24 June 2016