The former party president ended days of speculation by confirming his intention to stand following the Lib Dems' ballot box wipeout at the General Election.
Farron said he had spent the last six days listening to hundreds of party members who have been urging him to stand to succeed Nick Clegg, who quit after the Lib Dems secured just eight MPs last week - compared with 57 in 2010.
The Westmorland and Lonsdale MP joins former health minister Norman Lamb as a contender to replace Mr Clegg.
In his bid for support, Farron suggests the values the Lib Dems must fight for include freedom, equality, internationalism - with a focus on co-operation with Europe - and reform of the voting system, with a desire for a "new federalism".
On his website www.tim2lead.com, Farron said: "This is a critical moment for our party.
"The General Election was won by the politics of fear. We suffered a heavy defeat. Now we face the fight of our life: to prove we are relevant to people across the country, to show them what we believe and why we matter. We have to be clear about the values that set us apart."
Farron said he was proud of the party's coalition achievements although he was "saddened that it muzzled our voice", adding: "Like many people who have contacted me over the last few days, I am frustrated that we couldn't make the case for a fairer, greener, freer Britain."
He also confirmed his intention to run for leader during an interview with BBC Radio 4's Today programme and said the party fully accepts "the drubbing we got".
Farron went on: "I think what I am saying is there are thousands and thousands of people in this country who clearly woke up on the Friday and thought 'goodness me, we're not losing the liberals, we're not losing the Liberal Democrats', and that's why I'm standing for the leadership - because I believe that this party not only can be saved but it must be saved."
He recalled the fate of the Dutch liberals D66, saying they were able to recover after seven years to top the polls after facing a similar set of circumstances to the Lib Dems.
Farron said: "We know there is no God-given right for us to survive as a party or come back, but there is plenty of precedent for us to work from to make sure we have that comeback.
"And we're going to do it by building infrastructure and campaigning, having a kind of bloody-minded self-belief that we are going to recover and inspiring people to join us and step up to the mark.
"We know that we have fallen an awful long way short of where we want to be but absolutely Britain needs a liberal voice now more than it ever has, and I am determined that, fuelled by a sense of desire for justice, a belief in the rightness of our cause, I can inspire us to come back to the centre of British politics."
Farron said he has no plans to change the Lib Dems' name back to the Liberal Party.
Many of the Lib Dems' former cabinet ministers and potential leadership candidates, including Vince Cable and Danny Alexander, were among the electoral casualties on polling day.
To get on the leadership ballot a contender must secure the endorsement of 10% of MPs - now less than one person - as well as 200 members from at least 20 local Liberal Democrat parties.
The wider membership selects the winner in an alternative vote system, with the verdict due on July 16.