The Scottish Parliament has backed Nicola Sturgeon's call for the powers to hold a second independence referendum.
MSPs voted 69 to 59 to mandate the First Minister to seek permission from the UK Government for a ballot to be held between autumn 2018 and spring 2019.
Ms Sturgeon's minority Scottish Government won the vote following an extended debate thanks to support from the Scottish Greens.
But Prime Minister Theresa May has already said she will block another referendum while the Brexit process takes place, stating "now is not the time".
The two-day debate started last week but was suspended on Wednesday as news of the terror attack at Westminster emerged.
The vote comes the day after Ms Sturgeon met with Theresa May in Glasgow, and the day before the process for leaving the European Union will be formally triggered by the PM.
The First Minister has insisted her referendum timetable would allow Scottish voters to make a choice when the terms of the UK's exit deal become clear and before it is "too late to choose our own course".
Speaking before the leaders' meeting on Monday, Mrs May said her position will not change, arguing that a vote within Ms Sturgeon's proposed time frame would be unfair to voters and come at a time when the focus should be on securing the best Brexit deal for the whole of the UK.
Ms Sturgeon said she would delay making the section 30 request - the mechanism for the transfer of powers to hold the referendum - until ''later this week''.
She said she ''hoped the UK Government would respect the will of the Scottish Parliament'', but if it does not she will set out her next steps after the Easter recess.
Ms Sturgeon said: "It is now the will of Scotland's democratically-elected national Parliament that discussions should begin with the UK Government to enable an independence referendum to be held.
"Today's vote must now be respected. 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.
"We will now act on the mandate given to us by Parliament by making a formal approach to the UK Government within the next few days, after Article 50 has been triggered.
"This is, first and foremost, about giving the people of Scotland a choice on this country's future.
"The Prime Minister says that now is not the time for a referendum. I agree with that, which is why I have indicated a timescale no earlier than 18 months from now, when the terms of Brexit are clear - something the PM has now indicated she agrees with.
"It is up to the UK Government to now make clear when they consider a referendum would be appropriate."
UK Scottish Secretary David Mundell told BBC Scotland: "We won't be entering into any negotiations at all until the Brexit process is complete.
"Now's the time for the Scottish Government to come together with the UK Government, work together to get the best possible deal for the UK and that will mean for Scotland as we leave the EU.
"We're not entering into negotiations on whether there should be another independence referendum during the Brexit process.
"We don't have a crystal ball as to how long that process will take. We don't recognise, for example, 18 months as being a key point in the journey.
"It will be a journey that will involve the negotiations with the EU, it may be a journey that involves transitional measures, it may be a journey that will involve significant implementation time.
"It's not appropriate to have a referendum whilst people do not know what the future relationship between the UK and the EU is and they won't know that until the Brexit process is complete."