The Shetland MSP was one of only five LibDems returned at the polls, when the party's share of the vote collapsed by about 8% on 2007. Some 25 candidates lost their £500 deposits after failing to win 5% of the vote.
The LibDems won no constituency seats on the mainland. They had 16 MSPs in the previous parliament.
Former MP Willie Rennie, who was elected as a new list MSP from Mid-Scotland and Fife, is regarded as a likely candidate to replace Mr Scott, who will stay on as an MSP and has been tipped in some quarters as a possible presiding officer in the new parliament.
Mr Rennie may face a challenge from Orkney MSP Liam MacArthur. He and Mr Scott were the only LibDems to win constituency seats. The others returning to Holyrood are Alison McInnes, from the North East list, and Jim Hume in the South of Scotland.
Announcing his departure with immediate effect, Mr Scott said: "Thursday's Scottish general election result was disastrous and I must and do take responsibility for the verdict of the electorate. The party needs a new direction, new thinking and new leadership to win back the trust of the Scottish people."
Mr Scott has blamed Thursday's outcome on the unpopularity of the Coalition Government and his party's role in it. He made it clear at several points during the campaign that he felt he had been hampered by the "Nick Clegg" effect.
He said today: "There's just no doubt that since last May we have been up against it because of the formation of a UK government where the Liberal Democrats were seen to be propping up the Conservatives. And that's, I think, in Scotland, a pretty disastrous and toxic mix in politics. It's for the party now to decide how to move forward and I think that's best done with a new leader."
However, critics have also noted that he performed relatively poorly in the televised leadership debates.
Most commentators believe that a huge number of LibDem votes were successfully "poached" by the SNP, with nationalists claiming the scalps of many of Mr Scott's senior colleagues: finance spokesman Jeremy Purvis, chief whip Mike Rumbles, education spokeswoman Margaret Smith, and veteran MSP Mike Pringle.
Former cabinet minister Ross Finnie also failed to be re-elected from the West of Scotland list , and the LibDems lost their Glasgow list seat.
Mr Clegg, the UK LibDem leader and Deputy Prime Minster, said in a statement: "I was very sad to hear of Tavish's decision. He has been an excellent and energetic leader of the Scottish Liberal Democrats at an extremely difficult time, as well as a good friend and colleague.
"I'm sure he would have done a brilliant job leading the fight back for the LibDems in Scotland but I fully respect his decision. I know that Tavish will continue to play a central role in supporting the new LibDem leader in Scotland and in Scottish politics as a whole."
Former LibDem leader Charles Kennedy said Mr Scott was "handed mission impossible" in the Scottish elections, given the "current coalition unpopularity".
Paying tribute to him, Mr Kennedy said: "I am extremely sorry to learn of Tavish's decision to step down. He was handed mission impossible in the Scottish elections, given the current coalition unpopularity. That was always likely to be the case, as some of us warned at the time one year ago.
"Tavish is one of our country's most talented politicians and his response today is characteristically honourable. It deserves to be met by a response at a UK Liberal Democrat level which is similarly honest."
First Minister Alex Salmond said: "I have great respect for Tavish Scott, a distinguished parliamentarian with a significant contribution to continue making, and he carries my very best wishes for the future."
Scottish Labour leader Iain Gray, who is to stand down this autumn, added: "Tavish Scott has served his party energetically and I am sure he will continue to serve his constituents diligently and effectively. I wish him well for the future."
Mr Scott had held a string of senior posts in previous Scottish Parliaments. He served as a deputy minister in the first Holyrood administration but quit in protest at fishing policy. In the next Holyrood administration, he was back in ministerial office but faced calls for his resignation after appearing to break ranks with Executive policy, again over fishing.
Born in 1966 in Inverness, Mr Scott began his political career as a research officer for Jim Wallace in 1989. He served for two years as press officer for the Scottish LibDems and ran the party's election communications team in 1992.
He then returned to Shetland to take over the family farm and served as a councillor there until 1999 when he was elected to Holyrood.
Initially overlooked for a ministerial post, he became deputy parliament minister in 2000 but quit five months later over a decommissioning scheme for the fishing industry. On the backbenches, he found a new lease of life as a forceful interrogator on Holyrood's Enterprise Committee.
After the 2003 election he was the Lib Dems' chief negotiator during coalition talks with Labour. In August 2008, Mr Scott was elected leader of the Scottish Liberal Democrats after he secured 59% of the vote, outpacing rivals Ross Finnie and Mike Rumbles.
During this year's election campaign he spoke out against plans for a single police force for Scotland and said he was focused on jobs and education.
In the last televised debate before voters went to the polls, which was broadcast on STV on Tuesday night, he said people could decide on Thursday if they wanted a government that "absolutely drives" for independence and does that "every day for the next five years" in a political campaign, or if they wanted a government "that's about jobs, about education about keeping our services local".
Mr Scott divides his time between Shetland and Edinburgh, between two families. From his first marriage he has a daughter and two sons, aged 18, 17, and 11 respectively. The boys live in Shetland, his daughter is at university. He married again in 2008, to BBC journalist Kirsten Campbell. Their son, Archie, will be two in August.
His successor at Holyrood must be an MSP under the party's constitution. East Dunbartonshire MP Jo Swinson has been appointed acting leader meantime.
Mr Rennie scored a coup for his party in 2006 when the LibDems won the safe Labour Westminster seat of Dunfermline and West Fife in a by-election. After failing to hold the seat last year, Mr Rennie went on to work for a time as an adviser to Scottish Secetary Michael Moore.
A former student at Paisley College of Technology where he got involved in politics, Mr Rennie ran the Scottish Young Liberal Democrats and after graduation went on to work for the party in Cornwall.
He then went on to work for the Liberal Democrats' campaigns department before managing the party's campaigns in the south-west of England, securing the return of a sizeable number of new MPs in the 1997 General Election.
He moved back to Scotland where he was chief executive of the Scottish Liberal Democrats from 1997-9, and then the party's chief of staff in the new Scottish Parliament from 1999-2001. From 2001-6 he worked for communications firm, McEwan Purvis, helping advise the Royal Society of Chemistry and Asthma UK.
After his by-election success in 2006, he was a member of the LibDem shadow defence team, and also chair of their parliamentary campaigns unit.
He is a keen runner, and was runner-up in the 2006 Scottish Coal-Carrying Championships held in Kelty, Fife.
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