Nicola Sturgeon said becoming Scotland's next first minister would be "the greatest honour and an immense responsibility" as she confirmed she was standing to succeed Alex Salmond in the job.
He announced his intention to resign from the positions of both SNP leader and Scottish First Minister within hours of seeing voters in last week's referendum reject his dream of independence.
When nominations for the post of SNP leader opened this morning Ms Sturgeon, who was already the clear frontrunner for the post, formally declared her candidacy.
She is now in line to become Scotland's first female first minister, as well as the first woman to lead the SNP.
Ms Sturgeon said: " To be the first minister of my country, especially at this exciting and optimistic time, would be both a great honour - without doubt, the greatest honour - and an immense responsibility.
"I am putting myself forward for two simple reasons: I want to serve my party and my country. And I believe I am the best person for the job."
She added: "I also hope my candidacy, should it succeed, will send a strong message to every girl and young woman in Scotland: no matter your background or what you want to achieve in life, in Scotland in 2014 there is no glass ceiling on ambition."
Ms Sturgeon, who joined the SNP at the age of 16, has spent 10 years serving as Mr Salmond's deputy leader in the SNP, and has also been Scotland's Deputy First Minister since the nationalists came to power in 2007.
She told a press conference in Glasgow said she was now "more convinced than ever" that Scotland would become independent, as she dismissed any suggestion that the country could leave the UK via any other route than a referendum.
But she said the timing of such a vote could only be determined by circumstances, as she refused to state if under her leadership the SNP manifesto for the 2016 Holyrood election would include a pledge to hold another referendum.
Ms Sturgeon said: "Scotland will only become independent if the people of Scotland vote for independence in a referendum. There is no short cut to independence.
"But if the UK parties honour the promise of the last few days of the referendum campaign, we will travel a significant distance to independence.
"If certain things happen, if the UK Government reneges on the commitments made about more powers, if a European referendum takes, or threatens to take, Scotland out of the European Union, you may well have circumstances in which the people of Scotland will be demanding the right to choose a different future for Scotland."
But he political opponents said she had to move on from the SNP's "broken dream" of independence.
Labour MSP Drew Smith said: "If Nicola Sturgeon wants to move forward after so long as Alex Salmond's deputy she needs to show that she has learned the lessons of the referendum which her old boss has found so difficult to heed. That must mean being prepared to accept that Scotland remaining within the United Kingdom is the settled will of the Scottish people.
"Nicola Sturgeon should reflect that in any new agenda she seeks to set out."
Scottish Conservative deputy leader Jackson Carlaw said the independence was now in the "rear view mirror" behind the country, while the promise of new powers lay ahead.
He stressed it was more important for the Scottish Government to be involved in that process than to reflect "on its broken dream", adding: "People have moved on, the SNP must too."
Meanwhile Scottish Liberal Democrat leader Willie Rennie said: " The referendum vote demonstrated the will of the Scottish people to build a stronger Scotland and it will be for all political parties to match those expectations."
With the Conservatives, Labour and the Liberal Democrats all having promised the devolution of substantial new powers to Scotland in the days before the referendum, Ms Sturgeon warned the UK parties that they would face an angry backlash if they failed to deliver on this.
She said she would be a "willing partner for progress" in talks about transferring responsibility for more areas to Holyrood, but was also " equally clear what I believe Scotland expects of that process in return".
Ms Sturgeon, who is stepping down as SNP deputy leader to run for the party's top job, said the pro-UK parties had made a "clear and unmistakable" pledge that the package for Scotland would be "something near to federalism".
She stated: "Well, let me say this to Westminster on behalf of Scotland - it had better be.
"If the UK parties move forward in that spirit, they will have, in me, a willing partner for progress.
"If not, they will pay a heavy political price - not because I say so but because the people of Scotland will make it so."
Although she said the case for Holyrood having more powers was now "urgent and irresistible", Ms Sturgeon stressed that if she becomes First Minister "my responsibility will also be to use those powers we already have to make life better, now, for those we serve".
She pledged: "Any Government I lead will always take seriously its responsibility to make the very best of the limited powers at Holyrood, whilst also arguing Scotland's case for greater authority and the tools capable of transforming our nation."
She added: "If I am First Minister, my responsibility every single day I am in that job will be to govern well, wisely, creatively and innovatively with the powers I have at that time."