Mr Kennedy was driven out by his own MPs just 48 hours after finally being forced to confess to a long-running drink problem.
Momentum immediately began building behind deputy Sir Menzies Campbell, who became acting leader and announced he would stand for the full-time job.
Speaking at the party's Westminster headquarters, Mr Kennedy said he been "inundated" by messages of support from activists.
But he admitted: "It is clear now that such support is not reflected strongly enough across the Parliamentary party."
Mr Kennedy had hoped to survive by appealing over the heads of MPs to party members and calling a leadership contest when he made his public confession on Thursday night.
However, there were signs that the party grassroots also wanted him replaced.
In his statement he told reporters: "In all of this the interests of the party have to come first. That is where my personal, political and constitutional duty lies.
"Accordingly, I am announcing today that when nominations do open for the leadership of the party I shall not be putting my name forward. And I am standing down with immediate effect."
Sir Menzies, favourite to succeed him, was the only expected leadership contender to confirm he will stand.
Speaking outside his home in Edinburgh, Sir Menzies commended Mr Kennedy for his "dignity and courage" and for his achievements as leader of the Liberal Democrats over the past six years.
"Under his leadership the party has advanced to its best position for 80 years and the party will forever be in his debt," he said. " Today we must wish him and his family well."
Two fellow "shadow cabinet" members who had called on Mr Kennedy to go - Ed Davey, the education spokesman, and Treasury spokesman Vince Cable - signalled their support.
Environment spokesman Norman Baker and Lib Dem peer Lord Lester called for Sir Menzies to be returned unopposed.
However, party president Simon Hughes and home affairs spokesman Mark Oaten are also expected to contest the leadership.
Both were among those lining up to pay tribute to Mr Kennedy but declined to confirm they will stand.
Predecessor Lord Ashdown was also among those who praised Mr Kennedy's achievements in his six years in charge.
However, the resignation will be seen as a scalp for new Tory leader David Cameron.
Mr Cameron's early success intensified Lib Dem concerns about his laid-back style.
Although the party had its strongest showing for 80 years at the May general election many felt that their opposition to the unpopular Iraq war should have meant a major breakthrough.
When Mr Kennedy ignored private ultimatums to stand down, issued before Christmas, the fact that he was receiving treatment for a drinking problems was leaked to ITV News.
His decision to fight on infuriated colleagues prompting 25 MPs, including 21 frontbenchers, to yesterday warn they would not serve under him.
Even faced with the threat of mass resignations if he was not gone by Monday, Mr Kennedy insisted he could survive in a newspaper interview this morning.
However, his claim to "overwhelming" support from activists was challenged by a provisional YouGov poll showing 65% thought he should be replaced.
Mr Kennedy's spokeswoman was still insisting that there would be no further statement or appearance by him at 10.30am.
Then at 2pm she announced the then Lib Dem leader would be making a surprise statement from the party's Cowley Street HQ.
Mr Kennedy was tight-lipped as he left his London home with wife Sarah Gurling.
True to form, the statement came slightly later than scheduled but Mr Kennedy looked healthier, and happier, than he has done on many occasions in the past.
"I have been in politics far too long to be overly sentimental about this sort of moment," he said.
However, he went on to thank Anna Werrin, an aide since he entered Parliament 23 years ago, and wife Sarah, mother of his son Donald who was born during the election in May.
Mr Kennedy, MP for Ross, Skye and Lochaber, said he intended to stay on as "a loyal backbench Liberal Democrat".
He admitted the party has "serious internal political issues to address" about its future direction but insisted they were not "irreconcilable".
"A new leader inherits a party with the largest House of Commons representation in the liberal tradition in over 80 years," he said.
"We are established as serious players in the changing reality which is three-party politics across Britain.
"I believe that to be a good inheritance and a great opportunity. One in which I look forward to continuing to play my part."
As the couple arrived back at their London home, his wife said: "I am very proud of him, both personally and for what he has achieved for the party."
A timetable for the leadership election will be drawn up at a meeting of the Liberal Democrats' federal executive committee on Monday.
With local elections looming in May officials want the contest decided as quickly as possible.
It is likely to announce a two-week period for nominations to be accepted.
If Sir Menzies is challenged there will be a ballot of all 73,000 Lib Dem members using the single transferable vote system.Reuse content