Ms Eagle abandoned her leadership bid after getting fewer nominations from elected Labour members than Mr Smith, who now goes forward as the “unity candidate” to try to unseat Mr Corbyn.
Ms Eagle conceded she could not overhaul her rival and threw her support behind Mr Smith, urging people to take part in an election triggered by an unprecedented revolt among Labour MPs against their leader.
“We have a Labour Party at the moment that is not working, we’ve got a leader that doesn’t have the confidence of his members of parliament and isn’t reaching out to the country,” Ms Eagle said.
“We need to have a strong and united Labour Party so we can be a good opposition, take the fight to the Conservative government and heal our country.”
She said she would be campaigning alongside Mr Smith “with all my enthusiasm and might”. Mr Smith was nominated by 90 members of the parliamentary Labour Party, including 88 MPs. Labour did not provide official figures for Ms Eagle, but it is understood she was nominated by 63 MPs and nine MEPs. Mr Smith’s supporters included former party leader Ed Miliband.
Even with the full support of Ms Eagle and her backers, the MP for Pontypridd faces a daunting task. A YouGov poll published on Tuesday found Mr Corbyn would win a leadership election by 20 points regardless which of the two challengers he faced.
Mr Smith attempted to reach out to left-wing Corbyn supporters, saying he shared the Labour leader’s ideals but offered a better chance of winning the next election.
“I am just as radical as Jeremy Corbyn,” Mr Smith said. “I think Jeremy is owed a debt of gratitude for helping Labour rediscover its radical roots, but we do need a new generation of Labour men and women to take this party forward, to get us ready for government once more.”
He pledged to fight the leadership election “street by street, town by town, meeting by meeting” to convince Labour members he could lead a “credible, radical government-in-waiting”.
Supporters praised Ms Eagle for having the “courage” to force an election by being the first to stand against Mr Corbyn, before standing down in the interests of party unity.
Mr Smith said Ms Eagle was a “great Labour woman”, adding: “I absolutely cannot do without her in what will be a very difficult few months.”
Amid speculation the pair did a deal that will see Ms Eagle return as a senior member of the Labour front bench, Mr Smith said: “Angela is a star in the Labour firmament and she will be at my right hand throughout this contest and if I am successful thereafter Angela will be alongside me as my right-hand woman.”
Ms Eagle’s decision means the Labour party will continue to wait to have its first female leader.
Argument continues to rage over the rules governing who is allowed to take part in the leadership vote, both in terms of the candidate and the electorate.
A Labour donor and former parliamentary candidate, Michael Foster, is bringing a High Court claim in a bid to overturn a decision by the party’s National Executive Committee to assign Mr Corbyn a place on the leadership ballot without the need to secure nominations from elected members.
The Labour leader has asked a court to allow him to fight the legal action, which currently names the party’s general secretary, Iain McNicol, as the sole defendant.
His application to be added as a party to the proceedings as second defendant was heard by Master Victoria McCloud at a preliminary hearing.
Lawyers for Mr Corbyn stated: “His personal interest in the subject matter of this litigation is pressing and obvious and distinguishes him from the general body of members represented by Mr McNicol.”
A trade union is also considering legal action against an NEC decision it says has banned members who joined after 12 January this year from taking part in the leadership contest.
The committee has been accused of attempting to rig the leadership contest by changing the rules to prevent more than 130,000 new members from voting.
Shadow chancellor John McDonnell has said there was “widespread concern and anger” about the decision that only people who had joined the party before January this year could participate in the contest.
Manuel Cortes, the general secretary of the Transport Salaried Staffs Association said: “Those who joined after 12 January aren’t being allowed a vote in the leadership election. Yet Labour appears to be happy to take their hard-earned cash but appears to be hell-bent on denying them a voice.
“We will now consider what can be done to ensure our members are not disenfranchised. Sadly, this means seriously looking at seeking legal redress.”