But the SNP leader branded the Tories "terrified of Scotland's right to choose" as she warned their opposition will not stand.
Mr Johnson has written to the Scottish First Minister today stating that both Ms Sturgeon and her predecessor Alex Salmond had pledged that the 2014 referendum would be "once in a generation." event.
“The people of Scotland voted decisively on that promise to keep our United Kingdom together, a result which both the Scottish and UK Governments committed to respect in the Edinburgh Agreement," the Prime Minister stated.
The UK Government will continue to to uphold the democratic decision of the Scottish people and the promise that you made to them. I cannot agree to any request for a transfer of power that would lead to further independence referendums."
Ms Sturgeon made the request for a transfer of power, via a so-called Section 30 order, which would allow Holyrood to stage a second referendum in the aftermath of the SNP's election landslide victory north of the border last month. The First Minister had also demanded that power to stage referendums be permanently transferred to Holyrood.
But Mr Johnson's letter adds: "Another independence referendum would continue the political stagnation that Scotland has seen for the last decade, with Scottish schools, hospitals and jobs again left behind because of a campaign to separate the UK.
"It is time that we all worked to bring the whole of the United Kingdom together and unleash the potential of this great country."
But Ms Sturgeon insisted that the UK Government's position will not hold.
“The Tories are terrified of Scotland having the right to choose our own future," a spokesman said.
"They know that given the choice the overwhelming likelihood is that people will choose the positive option of independence. The Tories – and their allies in the leaderships of Labour and the Lib Dems – lack any positive case for the Union, so all they can do is try to block democracy. It shows utter contempt for the votes, views and interests of the people of Scotland and it is a strategy that is doomed to failure."
"The problem for the UK government is that the longer they try to block a referendum, the more they demonstrate that the Westminster union is not a partnership of equals and the more support for independence will grow. It will also mean for the Tories that the loss of half of their seats suffered at the recent general election – fought by them on the sole issue of opposition to an independence referendum – will be only the start of their road back to political oblivion in Scotland."
But Scottish Liberal Democrat leader Willie Rennie insisted that support for independence is no higher than it was in 2014.
He added: "The Scottish Liberal Democrats are on the side of the majority of people in Scotland do not want another independence referendum.
“What this country needs is a government that is focused on delivering excellent public services and a federal UK that ensures that power is shared across the whole of the country.”
The Scottish Greens are to launch their own Yes campaign at the end of the month and co-leader Patrick Harvie slammed Mr Johnson's rejection.
“It is absolutely appalling that we are to be ripped from the EU against our will, and utterly undemocratic that we are being denied a say on our future," he said.
"In 2014 the all-party Smith Commission accepted that nothing prevented Scotland becoming an independent country if the people of Scotland chose that path. Since then the Tories have been consistently rejected in Scotland, as has their Brexit project. The people of Scotland are sovereign, they alone have the right to decide their future.”
Pamela Nash, chief executive of Scotland in Union, said the majority of Scots don't want a divisive second independence referendum.
"It would lead to deeper divisions in society and cause further neglect of vital public services like schools and hospitals," she added.
"Scotland deserves better. Nicola Sturgeon should now focus exclusively on her devolved responsibilities and stop trying to inflict economic pain on communities."