She will face former cabinet ministers Ed Balls, Andy Burnham and David and Ed Miliband in the three-month contest.
'Huge surge'
Labour members, trade union members, MPs and MEPs will be balloted and the result announced on 25 September.
Until Wednesday morning Ms Abbott had only 11 nominations - well short of the number required to get on the ballot paper. However her bid was boosted when fellow left-wing MP John McDonnell withdrew from the race, saying he wanted to help her get through.It was tight, but we did it
Mr Miliband then said he would give her his support and encouraged others to do so - she has also been supported by acting party leader Harriet Harman, who said she wanted to see a woman in the contest.
Ms Abbott denied it was "patronising" to be helped onto the ballot by Mr Miliband, adding: "There's been a huge surge of letters and emails from party members saying that they wanted a diverse group of people running in this leadership contest and I think David Miliband and others responded to the feelings of the membership."
"There is nothing artificial about the party's and public's interest in my candidacy," she told the BBC News channel, adding that she expected to win backing "from across the party" once the contest got under way for real.
'Authentic strand'
She also told the BBC she had always been "quietly confident" she would get into the ballot - as there was a lot of support for not having "a panel of leadership candidates who all looked the same".
"It was tight, but we did it," she said.
Her success was welcomed by her fellow candidates. David Miliband said he had been "determined" to help Ms Abbott make it into the contest proper as she represented an "authentic strand" of opinion within the party.
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"It's time to turn the page from Blair and Brown - all the candidates believe that.
"It is not tokenistic," he said of her candidacy. "She has 20 years of experience and commitment. It is right she is on the ballot"
He said all the contenders must be ambassadors for Labour and be willing to engage in "dialogue and debate" not fight among themselves.
Ed Miliband told BBC News: "I think we need the widest possible contest and I am pleased that Diane is on the ballot."
But he said it was now time the contenders "stopped talking to themselves" and got on with making their case to the party membership.
'Too technocratic'
According to pre-released extracts of a speech he will give tomorrow, the former energy secretary will say it is time to "turn the page from Blair and Brown" and say there has been a "culture in our party that stifled dissent and debate".
He will say the contest is about "who can really move us on from a politics that was too technocratic and managerial and stopped inspiring, to one rooted in our values, more optimistic about the change we can make happen".
Andy Burnham, who also only made it over the vote threshold in the last few hours of nominations, said the Parliamentary Labour Party had "worked in a pragmatic way to get a lot of people on to the ballot paper" and Ms Abbott's presence would "liven up" the contest.
Commenting as nominations closed, acting Labour leader Harriet Harman said the leadership contest would be "open, engaging and energising". She said four million people were expected to vote in the contest, which would be "the biggest and most widespread election of any political party or any organisation in this country".
The leader is chosen by an electoral college system made up of three sections - Labour MPs and MEPs, party members and members of affiliated unions and other affiliated organisations.
People are balloted individually in each of the three sections, with the results from each making up a third of the final result.
Voting will take place between 16 August and 22 September and the winner will be announced on the first day of the party's conference in Manchester on 25 September.
