The vote by members of the Scottish Parliament gives the green light to First Minister Nicola Sturgeon to ask the UK Parliament for a referendum between autumn 2018 and spring 2019.
British Prime Minister Theresa May has indicated she will reject Sturgeon's timetable
. Britain is expected to leave the European Union in 2019, and May has said that "now is not the time" for a vote that could break up the United Kingdom.
"Today's vote must now be respected," Sturgeon said afterward, according to Britain's Press Association.
"The mandate for a referendum is beyond question, and it would be democratically indefensible -- and utterly unsustainable -- to attempt to stand in the way of it."
Sturgeon said the referendum should occur "no earlier than 18 months from now, when the terms of Brexit are clear."
"This is, first and foremost, about giving the people of Scotland a choice on this country's future," she said, according to the Press Association.
In a statement after the vote, the UK government said, "We should be working together, not pulling apart," and that it would not start negotiations now on a referendum.
"It would be unfair to the people of Scotland to ask them to make a crucial decision without the necessary information about our future relationship with Europe, or what an independent Scotland would look like," the statement said.
Changed political landscape
In a failed 2014 referendum on independence, Scotland voted 55% to 45%
to remain in the UK. But the Scottish National Party, led by Sturgeon, said the landscape has changed since Britain decided to leave the EU.
Sturgeon said the Brexit vote
is forcing Scotland out of the EU against its will as 62% of Scots voted in June to remain in the bloc
Opening the referendum debate last week in the Edinburgh Parliament, Sturgeon said it would be "wrong, unfair and utterly unsustainable" for the UK government to block her request.
There has been fierce opposition to a fresh referendum from the Scottish Conservatives, Labour and Liberal Democrats.
But the Scottish National Party, the largest party in the Parliament, will be backed by the Green Party, enabling Sturgeon to put May under increased pressure.
Clash between leaders
The two leaders met Monday in Glasgow ahead of the UK government's plans to trigger Article 50
on Wednesday, the formal announcement of a separation from the EU.
In comments reported by the Press Association, Sturgeon said May had been clear that the terms of the UK's divorce from the EU and the details of a new free trade deal would be known within two years.
"I think it makes it very difficult for the Prime Minister to maintain a rational opposition to a referendum in the time scale I have set out," Sturgeon said.