First Minister Alex Salmond declared it a "historic night" and said his party now has a mandate to widen Holyrood's powers.
In one of the most dramatic election nights Scotland has seen, the true scale of the victory was underlined as Labour was humbled in Glasgow as the SNP's newly dubbed 'magnificent seven' swept to victory.
The Nationalists took Anniesland, Cathcart, Kelvin, Shettleston and Southside, as well as two seats on the Glasgow list.
As the Evening Times went to press, 58 of the 73 constituencies, and two of the eight regional lists had been declared, with SNP returning 46 MSPs, Labour 20, Conservative five, Lib Dems two, Green Party one and independent one.
There has been a sea change in the political map of Scotland with traditional Labour heartlands such as Glasgow, Ayrshire and Lanarkshire sweeping to the SNP.
Alex Neil who won the Airdrie and Shotts constituency in Lanarkshire described the SNP's performance across Scotland as "a political tsunami".
Mr Salmond, 56, has declared Labour's Scottish heartlands are "gone forever", but said he was not taking the SNP's election success for granted until every vote was counted.
He said: "Scotland has now outgrown the Labour party."
Overall turnout plunged below 50% with the rain keeping voters away from polling booths. After two weeks of unbroken sunshine, the day of the Scottish Parliamentary elections saw the heavens open, but the gloomy weather could not dampen the SNP's rejoicing of their resounding success.
And Labour today pointed the finger of blame at the weather, admitting that a sunny May day would have helped them to mobilise their vote.
The party had emphasised the high number of people who had yet to decide if, or how, they would vote in the Holyrood elections.
While the turnout in the 2007 election was 52%, indications from early returns from constituencies such as Rutherglen, Uddingston and Bellshill showed that around 45% had turned out to vote.
In Dunbartonshire's Clydebank and Milngavie, Gil Paterson of the SNP sensationally beat Labour's Des McNulty for another SNP gain
Mr Salmond was resoundingly re-elected to Aberdeenshire East with 19,533 votes, a majority of 15,295.
Two of the earliest casualties of the night came as former Labour government ministers Andy Kerr and Tom McCabe were defeated by the SNP in a humiliating night for Iain Gray's party.
Meanwhile, Labour leader Iain Gray hung on to his East Lothian seat by the skin of his teeth with a majority of just 151 votes.
Finance Secretary John Swinney and Environment Minister Roseanna Cunningham swept to victory in the Perthshire North and Perthshire South and Kinross-shire seats respectively, both scoring massively increased majorities.
They were followed by more SNP victories in Clydesdale, where Aileen Campbell defeated Karen Gillon; and Airdrie and Shotts, where Alex Neil beat Karen Whitefield by even larger majorities.
Jamie Hepburn added to the SNP tally by beating Labour's Cathie Craigie in Cumbernauld and Kilsyth.
On a bad night for the LibDems, the only two early bright spots were victories for party leader Tavish Scott in Shetland and Liam MacArthur in Orkney.
The Conservatives' David McLetchie lost his Edinburgh Pentlands seat to the SNP's Gordon MacDonald.
Ms Sturgeon said the SNP's wins were a victory for "positivity over negativity".
She added: "We will make sure we can unite Scotland and take the country forward.
"The scale of the majority exceeded all my expectations. The people of Glasgow Southside have put their trust in me and I will repay that trust."
The final outcome of the election will be announced this afternoon.
Early today Mr Salmond said he was "delighted" with the results.
He added: "It is clear from the indications we have had so far that it is likely that the SNP has been bestowed trust by the people in a way that no party ever has before in a Scottish election.
"We'll take that mandate and that trust forward. We will take it forward to increase the powers of our parliament."
He added: "Positive campaigns will always beat a negative campaign and I hope that's a lesson that Scottish politics will long remember."
The Liberal Democrats suffered heavy losses in councils in the north of England, as Labour made gains in the English local elections.
In the Welsh assembly election, Labour made gains at expense of Plaid - but the party expects it to be "very tight" to get the 31 seats needed to claim an overall majority.
Voters were also taking part in the referendum on introducing the Alternative Voting system for electing MPs to Westminster. The outcome of that vote will be announced at around 8pm today.
Salmond given a dream mandate
Holyrood 2011 will go down as one of the most dramatic nights in Scottish election history.
If the overnight pattern of results continues today, Alex Salmond could even become the first party leader since devolution to have an overall majority in the Scottish Parliament.
Even if he doesn't achieve that he is likely to be able to depend on the help of parties such as the Greens and Independent Margo MacDonald, whose results will be known when the regional lists are calculated.
Mr Salmond is on course to have a mandate he could only have dreamed of at the start of the campaign to greatly widen the SNP's powers.
On the question of a referendum on independence, he said the immediate priority for the SNP would be to put "economic muscle" into the Scotland Bill.
He added: "In due course, in due time, of course we'll offer the Scottish people their chance to decide their own country's constitutional future."
Mr Salmond will also have the remit he wants to drive through policies such as minimum pricing on alcohol, which was defeated by Labour and the Conservatives.
The 56-year-old led the SNP to its first national election victory in 2007, beating the incumbent Liberal Democrat MSP for Gordon in the process.
For Labour, the defeat means another five years in the wilderness and the heavy losses will almost certainly see Iain Gray resign as leader.
The crisis facing the LibDems is just as great and Tavish Scott's leadership may also be in question, while Tory leader Annabel Goldie will also be looking closely at the regional list results.
