Lib Dem frontbencher Chris Huhne has launched his bid to become party leader saying: "I've decided to give it a go."
Mr Huhne said he would be campaigning for a fairer and greener society, and giving power back to the people.
Meanwhile home affairs spokesman Nick Clegg, who along with Mr Huhne is seen as one of the strongest contenders, is expected to launch his bid on Friday.
The race was sparked by the resignation of Sir Menzies Campbell, who blamed the media's obsession with his age.
Environment spokesman Mr Huhne, who is the first Lib Dem to break cover to announce his candidacy, said he wanted the party to be committed to the idea that "everybody's individual worth and chance is given its full possibility".
The green agenda, for which he is known, will play "a big part in the campaign", he said.
"And of course no Liberal Democrat could possibly stand for the leadership without stressing the importance of freedom - not just of course from oppression, a bossy and intrusive state, but also .... a fairer and greener society where we put people in charge.
"Too many people feel they don't have control over their own lives.
"Frankly it is disgusting that a child born into poverty has a life sentence. I also think too many people are imprisoned by bad luck and lack of opportunity and I want to free them.
"We need a clear champion who can make that case, and that's why I want to lead the Liberal Democrats."
Mr Huhne, who came second in the last leadership race 18 months ago, said he believed Sir Menzies had been given "a bad and raw deal in the public perception".
But he denied having anything to do with the ex-leader's demise, saying during a meeting last Thursday Sir Menzies had thought he "had been scrupulously loyal and there was no suggestion of any slur on my integrity in that matter".
He and Mr Clegg, seen as a fellow frontrunner, were "very much part of the same team".
Earlier acting leader Vince Cable, transport spokeswoman Susan Kramer and elections co-ordinator Ed Davey had all said they would be not running.
And former Lib Dem leader Charles Kennedy, 47, still popular among grassroots Lib Dems, said it was "highly unlikely" he would stand again, adding: "You should never say never in politics, but as close to never as you can get."
Nominations opened on Tuesday, with other possible runners including party manifesto writer Steve Webb and backbencher John Hemming.
'Irritated and frustrated'
Mr Cable, 64, said he had concluded that an older candidate would not be electable because of the "irrational prejudice" about age that had dogged Sir Menzies' leadership.
Ms Kramer, 57, a former London mayoral candidate, said she had decided not to put her name forward.
And Mr Davey, 41, said: "Having discussed things with my wife and colleagues, the imminent birth of our first child must take priority over politics and so therefore I have decided not to stand."
Sir Menzies said he had an idea who he wanted to succeed him
He offered his support for Mr Clegg, who he said would be "an inspirational leader for his party".
Mr Clegg, 40, has said he needed time to talk to his wife Miriam and close friends before deciding whether to stand, but is expected to launch his leadership campaign on Friday
In a BBC interview on Tuesday, Sir Menzies said he had resigned because the media's obsession with his age made it very hard to get policies across, adding that he was "irritated and frustrated" at having to step down, after 18 months in the job.
Asked if he thought he would have been forced out, had he decided to stay longer, he said he could not speculate about the future, but added: "I had no sense that there were people wanting to move against me."
Party president Simon Hughes, who has stood for the leadership twice before, ruled himself out of this contest earlier this week.
Nominations close on Wednesday 31 October and those with sufficient backing will put their case to party members.
Ballot papers will be sent out to Liberal Democrats across the UK from 21 November and the winner will be announced on 17 December.