" We are the party of the future and this decade can see us as the party of the governance of our country "
Speaking on the steps of the party's central London headquarters after what he described as "a fantastic victory", Mr Kennedy said the election had been a referendum on the opposition as well as on the government.
The election results showed the Lib Dems had "moved up a league" - and the country would in future judge the party by a higher standard, he added.
The Lib Dems have won 52 seats - six more than in 1997.
Addressing cheering supporters, Mr Kennedy ambitiously suggested that "we are the party of the future and this decade can see us as the party of the governance of our country".
But he also expressed concern about low voter turnout and the relatively high levels of support for the British National Party in Oldham, the scene of recent race riots.
Mr Kennedy was re-elected in his Ross, Skye and Inverness West constituency, winning more than 18,800 votes and trebling his majority.
The Lib Dems were overjoyed with their results which included holding onto Kingston and Surbiton in London with a huge majority and gaining a clutch of new seats nationwide.
But their joy was tempered by losing Taunton in Somerset and the Isle of Wight to the Tories.
The Lib Dems snatched Teignbridge, Guildford and Cheadle as well as Mid Dorset, Poole North, Ludlow and North Norfolk from the Conservatives.
And they were jubilant at wresting from Labour the Chesterfield seat formerly held by the Labour veteran, Tony Benn.
The former cabinet minister stood down as an MP when the election was called.
And the Lib Dems also managed to hold on to Romsey, won from the Conservatives in a sensational by-election result last year.
As the results continued to be called, Mr Kennedy said it had been a historic night for Labour, and congratulated Prime Minister Tony Blair on his success.
"It is also a doubly historic night for the Liberal Democrats in that we have in all likelihood built on the amazing breakthroughs of four years ago," he said.
Former Liberal Democrat leader Sir Paddy Ashdown said it had been a "terrific night" for his party.
Lib Dem gains compared with 1997
"What we can celebrate tonight is the best result since the 1920s and a vindication of Charles Kennedy's campaign," he said.
The two disappointments for the Lib Dems came at Taunton where Jackie Ballard was ousted by Adrian Flook and the Isle of Wight where Dr Peter Brand lost to Andrew Turner.
In Romsey, Lib Dem Sandra Gidley held onto the seat she had won in a sensational by-election gain from the Conservatives with a 12.6% swing from the Tories in May 2000.
In Kingston and Surbiton Edward Davey won a spectacular victory by holding onto his seat with an increased majority of 15,676 - compared with 56 in 1997.
Deputy First Minister of Scotland Jim Wallace said of Mr Davey's success: "I have a lump in my throat. I have never got near the majority of Ed Davey in four elections."
Meanwhile David Rendel held Newbury - a seat he took from the Tories at a by-election in 1993.
In Cheadle, the Lib Dems gained the seat from the Conservatives with a majority of just 33.
In Teignbridge, in Devon, Richard Younger Ross took the seat from former Tory minister Patrick Nicholls.
In Ludlow, Matthew Taylor wrested the seat from Conservative Martin Taylor-Smith.
And the party dealt a further bitter blow to the Tories by holding Torbay in the South West - one of the seats at the top of the Conservatives' target list.
Lib Dem Adrian Sanders increased his majority in Torbay from only 12 in 1997, to 6,708 - a swing of 7.5%.