In a surprise move, Ms Abbott said she was confident of attracting the 33 nominations needed to get her on to the ballot paper.
She becomes the sixth participant in the contest, after David Miliband, Ed Miliband, Ed Balls, John McDonnell and Andy Burnham.
There had been concern in the party at the lack of a female challenger to take over from Gordon Brown as Labour leader.
Harriet Harman and Yvette Cooper have said they will not stand.
Speaking on BBC Radio 4's Today programme this morning, Ms Abbott said: "We need to speak to our supporters and speak to our members in a way that we are not speaking to them up until now."
Of her prospects, she added: "We think that we can get the 33, because I am attracting support not just from the Left but from women and other MPs that want to see a more diverse range of candidates."
Ms Abbott, 56, was the first black woman MP when she joined the Commons in 1987. She is a member of the Socialist Campaign Group, of which Mr McDonnell is chair.
She said: "I'm going to run. So many people in the past 48 hours have asked me to put my hat in the ring and I have finally decided to do so."
The Hackney North and Stoke Newington MP said Labour needed the "broadest possible" contest as it debated the future of the party after this month's general election defeat.
"We can't go forward with a leadership debate where there is no woman," she said.
Ms Abbott insisted her bid was "perfectly serious".
She said none of the current frontrunners in the race would admit that the immigration system is "still inefficient and unfair and brings abuse, but nobody will say we have to address the underlying issues behind black and white working class unease about immigration, about housing, job insecurity.
"And, you know, if we are going to have a debate about immigration, I am the child of immigrants. Don't the millions of British people who are the children of immigrants have a voice in this debate also?
"I could not be more serious."
Mr Burnham, the former health secretary, launched his bid for the Labour leadership last night with a pledge to create a "People's Party".
In an article for the Daily Mirror, he said he would put an end to "stage-managed" politics run by "elites".
Mr Burnham insisted he could be a "unifying" force for the party, suggesting that - unlike most of his rivals - he had never taken sides in the Blair-Brown infighting.
"I am a team-player; I've never had time for factions," he wrote.
"That's why I can help make Labour welcoming and unifying, a voice for all people who want to get on in life but also want to live in a country fair to all - with a more even spread of health, wealth and life chances."
The Leigh MP said Labour had to "open up to more people".
"We must become a new kind of Party that involves and consults its members on a daily basis - truly a People's Party - and reduces the influence of small elites at the top," he insisted.
"We should bring down the final curtain on the era of stage-management in politics, making our party conference a forum for real debate and drama once again."
Ms Abbott suggested that most of the other leadership candidates, as former ministers, were incapable of accepting where the party had made mistakes in government.
She also indicated that she would be seeking to appeal to the female vote.
Asked what she was standing to represent, she said: "We have to stop allowing the Tories to position themselves to the left of us on civil liberties, we have to bring back democracy to the party.
"We have to address... the Labour movement has changed, the majority of members of our big industrial unions are women, we need to talk directly towards women and women workers.
"And we need to accept, in a way that past ministers cannot accept, what we did wrong in the past 13 years."
Former chancellor Alistair Darling said it was "good" that there was a broad range of Labour opinion being represented in the leadership contest.
"I think, as Diane knows, we don't always see eye to eye on everything but I think it's a good idea that every strand of opinion in the party should be represented," he told Today.
"This is a time when we will be choosing the next leader who will be here for some years.
"I'm all in favour of all strands of opinion being heard, whether or not I agree with every candidate who stands."
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