Alex Salmond resignation: Politicians react to first minister's statement
Prime Minister David Cameron has praised departing First Minister Alex Salmond's "huge talent and passion".
Mr Salmond is also standing down as SNP leader after voters rejected independence.
Nicola Sturgeon, his deputy in both roles and the favourite to replace him, said she could "think of no greater privilege" than to lead the party.
UK Labour leader Ed Miliband said Mr Salmond had been a "formidable frontline politician".
Mr Salmond made his announcement at his official residence in Bute House, Edinburgh, after the "No" side won Thursday's referendum by 2,001,926 to 1,617,989 for "Yes".
The national split of the vote was 55% for "No" to 45% for "Yes".
Mr Cameron said Mr Salmond had been "an effective first minister and always fights his corner".
He added: "While we disagree profoundly about his goal of a separated Scotland, and many other things, I respect and admire his huge contribution to politics and public life."
UK Labour leader Ed Miliband said: "Whatever our disagreements, he always spoke his mind and he has always stood up for what he believed in."
Scottish Labour leader Johann Lamont added: "Alex Salmond turned a minority party into a party of opposition into a party of government and was responsible for there being a referendum on Scotland leaving the United Kingdom.
"He has undoubtedly been an immense figure in Scottish political history."
Ruth Davidson, the leader of the Scottish Conservatives, said Mr Salmond's "decision to step down will help our country come back together again".
She added: "I am pleased that the first minister says he will continue to serve in Scottish politics.
"Scotland will benefit from his experience and service as we move forward."
Mr Salmond said he would resign as SNP leader at the party's conference in November.
He will then stand down as first minister when the party elects its next leader in a membership ballot.
Ms Sturgeon is seen as a clear frontrunner to replace him.
In her statement, she paid tribute to her "friend, mentor and colleague for more than 20 years".
"He led the SNP into government and has given our country a renewed self confidence," she said.
She added: "Alex's announcement today inevitably raises the question of whether I will be a candidate to succeed him as SNP leader.
"I can think of no greater privilege than to seek to lead the party I joined when I was just 16. However, that decision is not for today."
Finance Secretary John Swinney told BBC Scotland Mr Salmond had delivered "astonishing gains" for the SNP and "astonishing improvements" for Scotland.
Scottish Parliament Presiding Officer Tricia Marwick said: "Members from across the chamber will recognise the first minister as an outstanding parliamentarian and will join me in recognition of his substantial achievements and public service as an MP, MSP and as Scotland's longest-serving first minister.
"He will bow out following the most remarkable national debate and democratic renewal of our nation."
Welsh First Minister Carwyn Jones said Mr Salmond would "leave a large gap in Scottish politics".
"He is an astute politician and was a passionate leader of his party and the Scottish government," Mr Jones added.
Scottish Green Party co-convener Patrick Harvie paid tribute to Mr Salmond's role in "changing our political landscape".
Scottish Trades Union Congress General Secretary Grahame Smith said: "Alex Salmond has been a dominant figure in Scottish politics for over two decades.
"Whatever you think of his politics you cannot deny his political achievements."