She had written to the prime minister after her party the SNP won a huge majority in Scotland, claiming there was now a "democratic case" for a new independence poll.
But on Tuesday the prime minister flatly rejected her request for powers to be transferred to Holyrood, which would allow for a new referendum.
He told her he had "carefully considered and noted the arguments" she set out in her December 19 letter, but said agreeing to her request would lead to continued "political stagnation" in Scotland.
He told the first minister her predecessor Alex Salmond had made a "personal promise" that the referendum in 2014 - which he lost by 55% to 45% - was a "once in generation" event.
Mr Johnson said the government would "continue to uphold the democratic decision" made by the Scottish people and keep the "promise" made to them.
But Ms Sturgeon, who has previously refused to rule out legal action in a bid to force a second independence vote, said the Scottish Government would set out the next steps it will take before the end of January.
She said the Scottish Government would again ask MSPs at Holyrood to endorse "Scotland's right to choose".
"The people of Scotland will get the right to decide our own future in an independence referendum," the SNP leader said.
"The Westminster union cannot be sustained without consent. Democracy will prevail.
"The only question is how long it will take the Tories and the rest of the Westminster establishment to accept that inevitability."
Michael Gove, one of Mr Johnson's most senior allies in Cabinet, said Ms Sturgeon should "concentrate on the day job" rather than independence.
He went on: "The Scottish government is failing when it comes to education, health, transport and crime."
"What Nicola Sturgeon is terrified of is talking about anything other than independence, she is a one club golfer, a one trick pony - whatever the question, she always comes up with the same answer: IndyRef2."
The PM said a fresh "campaign to separate the UK" would see Scottish schools, hospitals and jobs "again left behind".
He added: "The UK Government will continue to uphold the democratic decision of the Scottish people and the promise that you made to them. For that reason I cannot agree to any request for a transfer of power that would lead to further independence referendums."
"The problem for the Tories is the longer they try to block democracy, the more they show the Westminster union is not one of equals and fuel support for independence.
"This response predictable - but also unsustainable and self defeating. Scotland will have the right to choose."
Scottish Labour leader Richard Leonard said it would "spectacularly naive" to think Mr Johnson's refusal to grant consent would "close the issue down".
Instead he said it would "only inflame the debate" about Scotland's future, adding: "The people of Scotland rejected independence in 2014 but Scotland remains divided.
"I believe that home rule within the UK is the only viable option that stands a chance of healing the divisions in our society.
"We can't wait for a UK Labour Government to deliver this so we must demand it now and mobilise for radical change."