Mr Farron hopes to stake a claim on the centre ground of politics in the wake of Jeremy Corbyn's election as Labour leader as the party bids to bounce back from a devastating election mauling in May.
Former business secretary Sir Vince Cable has called for Labour MPs dismayed by the rise of Mr Corbyn to join forces with the Liberal Democrats in a new alignment of centre-left parties against the Conservatives.
Tim Farron said Britain needed 'desperately' a party like the Lib Dems
Arriving on the first day of the party's autumn gathering, Mr Farron said: "The message here is very clear: we have the biggest space in politics open to us for a generation.
"Britain desperately needs a party that is liberal, progressive and economically responsible. We will fill that space.
"I'll be calling upon the Liberal Democrats here to steel themselves. Having had the result in May, against all the odds we matter more than we have done for perhaps a generation."
As the party faithful gathered in record numbers under sunny skies, Sir Vince told The Guardian: "This has all happened very quickly and I think what I would simply want to acknowledge is that there is a progressive centre-left out there but it is at the moment fragmented.
"And unless it is in some way effectively unified, the Tories will just have a monopoly on power."
The Liberal Democrats were left reeling in May as their 56 MPs were reduced to a rump of just eight, triggering Nick Clegg's resignation as leader following five years in government.
In his first conference appearance as leader, Mr Farron will attempt to rally the party's activists, insisting that the surge in membership since the election is the sign of a fightback.
At the conference's opening rally, he will say: "Britain is teeming with liberals, some of them are not yet in the Liberal Democrats. Some of them are in other parties. But we are their home."
The party's membership has grown by 20,000 to 61,000 since the election. A record 2,500 members are expected at the five-day conference.
In a sign that he does not believe Labour can win the next election under Mr Corbyn, Mr Farron will say: "We once again see the prospect of a decade or more of Tory rule, and it fills us with dread.
"So we have no right to sit in a comfort zone, every family whose home is at risk because the Tories undermine the recovery that we built; every desperate refugee turned back at the port; every business facing ruin if we leave the EU, every one of them is depending on us.
"We are liberals, we correctly talk a lot about rights, but we have a duty. Our duty is to claim the mantle of the credible progressive alternative to the Tories."
The Lib Dem leader, who will face a test of his authority at the conference by opposing a motion calling for the UK to give up its nuclear deterrent, risks another row with the grassroots over aviation policy after indicating he could back expansion of airports around London.
Party activists had previously ruled out airport expansion in south-east England.
But while Mr Farron maintained his opposition to an extra runway at Heathrow, he said he was "open-minded" about other options for increasing capacity around the capital.