The third, broadcast by the BBC from the Midlands, will be moderated by Question Time host David Dimbleby and deal with the economy.
BBC political editor Nick Robinson said the debates on policy detail should provide some answers for viewers but complex rules would limit the role of the audience and the moderator.
Applause will be restricted to the beginning and end of the debates and the audience will not be allowed to respond to leaders' answers.
Broadcasters drew lots to determine the order of the debates and the themes while the parties drew lots for the order of speaking - Lib Dem leader Mr Clegg will open the first debate, Mr Brown the second, and Mr Cameron the third.
Mr Brown welcomed the news that agreement had been reached, saying: "I'm so optimistic about the future of our country that I relish the opportunity to debate the big issues and to set out my vision about what we as a country can achieve together, and then let the people decide."
All involved were very clear that these were events which should and could add to the understanding of voters as they make up their minds
Mr Cameron said he was "absolutely delighted" about the debates. He said: "I think people have got a right to look at the people putting themselves forward as our next prime minister and to see the choice and to see the change that we could make and to make up their own minds."
For the Lib Dems, Mr Clegg said the debates would allow leaders to be put under "real scrutiny".
"I think these debates will give people the chance to have a really good look at the leaders, their values, their character, their judgements, their policies, before they make up their mind how they are going to vote at the ballot box," he said.
'Second class citizens'
The BBC is to hold separate party leader election debates in Scotland, Wales and Northern Ireland and other parties will be able to respond to the debates on the news.
But for the SNP, Angus Robertson said: "London-based parties are going to receive exponentially more exposure and coverage than other political parties, I think licence fee payers and voters in Scotland will be asking themselves why they are being treated as second class citizens."
And Welsh Assembly member Elin Jones, for Plaid Cymru, said the debates were being set up "in a way that will mislead people into thinking that only the London parties are taking part in this election".
"In many constituencies in Wales, this election will be a two-horse race between Plaid Cymru and one other party, yet that will not be reflected in these debates," she added.
The sessions will be broadcast on weekday evenings, in the final three full weeks of the election campaign - exact dates will be decided once the prime minister calls the election, widely expected to be held on 6 May.
Party leaders will open with a one-minute statement, then take questions from the audience, studio and public via e-mail.
They will have a minute to answer the question, a minute to react, and four minutes of free debate.
All questions - those on the main themes, and those from audience members and via e-mails - will be selected by a panel of senior journalists.
Handshakes between the candidates will be restricted to the end of the programme.
A spokesperson for the joint broadcasting panel welcomed the agreement, adding: "We were delighted by the positive atmosphere in all our dealings with the parties over the last few months, and the agreement we are jointly announcing today represents a major step forward in the way election campaigns can reach the entire population."
The broadcasters have jointly appointed the market research company ICM to recruit an audience with a broad cross-section of views.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.