Officials confirmed they were arranging a meeting between Alex Salmond and David Cameron within weeks to sign an agreement after nine months of stalemate.
A meeting between Ms Sturgeon and Scottish Secretary Michael Moore will take place next week to "pave the way" for the two leaders' summit, a Scottish Government spokeswoman said.
The developments came after an initial meeting between Ms Sturgeon and David Mundell, the Scotland Office minister, in Edinburgh yesterday and were taken as a sign that agreement has almost been reached.
In an upbeat statement afterwards, Mr Mundell said: "We had a very constructive meeting with the Scottish Government this morning and the momentum is definitely moving towards getting a deal to deliver a legal, fair and decisive referendum for Scotland.
"We discussed the timetable required to get the Section 30 order in place and agreed officials from both governments will now work to draft a memorandum of understanding on progress to date and to detail the areas which still require work.
"There will be a further meeting between the Secretary of State for Scotland and Nicola Sturgeon next week which will continue to make headway on the referendum issue."
A Scotland Office source said: "The feeling here is that we are glad to have the pace upped."
The First Minister's chief spin doctor said: "Mr Salmond expects to meet the Prime Minister in the next few weeks to bring a conclusion to the talks on the referendum."
Referring to the First Minister's comments on Tuesday, when he spoke of "concluding" talks within weeks, the spokesman added: "That was a clear signal from the First Minister that he expects a resolution to this sooner rather than later."
A Scottish Government spokeswoman said: "Nicola Sturgeon has agreed a meeting with the Secretary of State next week, paving the way for a meeting between the First Minister and Prime Minister in the next few weeks.
"Officials on both sides are advancing that in a number of areas."
The two governments have been at odds since the start of the year over the format of the planned independence referendum.
The UK Government has offered to devolve specific powers, making a Yes/No poll legally watertight.
But the Scottish Government has refused to accept, saying it would consider demands for a multi-option referendum, including a question on devo max.
The quickening moves towards a deal came hours after Ms Sturgeon – who is known to be less enthusiastic about the two-question format – started her new job as Constitution Minister.
They followed growing speculation that ministers were preparing to settle for a straightforward Yes/No question on independence.
A meeting between the First Minister and Prime Minister by mid-October would allow the so-called Section 30 powers to pass through both Westminster and Holyrood.
The prospect of a single question poll alarmed the Electoral Reform Society (ERS). It claimed it was "surreal" that enhanced devolution would not feature in the referendum.
Willie Sullivan, director of ERS Scotland, said: "The last thing we need here is a politicians' fix."
l Yes Scotland rounded on the CBI after its director-general, John Cridland, compared the plight of an independent Scotland to Slovakia losing 4% of its GDP in the first year after the break-up of Czechoslovakia.
A senior strategist at the Yes Scotland campaign accused Mr Cridland of "half-truths and scaremongering".