The Scottish Government tweeted a picture of the First Minister with her feet up on a couch in her Bute House residence writing the Section 30 letter.
This week, MSPs voted 69 to 59 in favour of seeking permission for an independence referendum to take place between autumn 2018 and spring 2019.
Ms Sturgeon said her mandate for another vote is now "beyond question," and warned it would be "democratically indefensible and utterly unsustainable" to attempt to stand in the way.
Scottish Secretary David Mundell said the UK Government would decline the request.
Ms Sturgeon is pressing ahead with a formal approach for a section 30 order — the mechanism for the powers to hold a referendum.
The Scottish Government tweet read: "First Minister Nicola Sturgeon in Bute House, Edinburgh, working on final draft of Section 30 letter to Prime Minister Theresa May."
It is expected to be sent to Downing Street on Friday.
Around 62 per cent of Scottish voters backed the UK remaining part of the EU in June 2016 and the SNP manifesto for last year's Holyrood elections made clear another ballot on independence should take place if there was a "material change in circumstances" from the previous ballot in 2014.
The example cited was for Scotland to be removed from the EU against its wishes.
Scottish Conservative, Labour and Liberal Democrat politicians are opposed to another referendum and the Prime Minister has repeatedly said "now is not the time" for another vote, indicating she will reject the SNP's preferred timetable.
After the vote in the Scottish Parliament, Ms Sturgeon said she would set out her next steps to Holyrood after the Easter recess if she is rebuffed in the Section 30 request.
The vote followed a meeting between Ms Sturgeon and Ms May in Glasgow and came the day before the process for leaving the European Union was formally triggered.
Additional reporting by Press Association
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