The former shadow business secretary is hoping to oust Jeremy Corbyn amid warnings the bitter rows over the party leadership could lead to a legal wrangle or lasting split.
The Labour leader has vowed to fight any challenge and continue in his position despite the overwhelming majority of his MPs losing confidence in his ability to secure a general election victory.
Explaining why she is challenging Mr Corbyn, Ms Eagle said “I just don’t think we are communicating with our voters”, and she added: “We have got to rebuild hope together and I think the Labour Party - when it’s working properly, when it’s functioning - that’s what it does and that’s what I want to see it get back to.”
She said: “The Labour Party needs to be saved - I’m stepping up to the plate to say it’s about time that we did this so we can make the Labour Party relevant again and so we can contend for government.
“I want to ensure our country can be healed after the terrible shock that Brexit is going to inflict on it.”
Ms Eagle, who will launch her campaign in London on Monday, told the Daily Mirror: “I think it’s important we all have our principles... but you also have to be in a situation where you can speak to Labour voters and the wider country - and give our party the best chance of being able to make that difference that early Labour governments made.
“We’ve all stood on the shoulders of what Labour governments in the past have done - if we’re not in government we can’t spread those chances around our society more widely.”
Ms Eagle has the backing of the 51 MPs needed for a formal challenge but it remains unclear whether Mr Corbyn will also have to secure the support of MPs in order to fight the leadership battle.
She said she believes she “would be a good prime minister for Britain”, and added: “In order to heal our country, we have got to ensure we change the Labour Party so that we can do that historic task - and I think I am the person to do that.”
The 55-year-old said her background as a “good, sensible, down-to-earth woman with Northern roots” would help her lead the party.
“I have got life experience and values. I’m a woman from the working class North; I understand metropolitan things too,” she said.
“I’m a gay woman - I know the difference between hope and fear.”
Meanwhile, Owen Smith, another potential leadership contender, is seeking crisis talks with Mr Corbyn as he claimed the leader and his allies are prepared to split the party in order to remain in place.
In a further sign the party is on the verge of all-out civil war, Mr Smith said that at a meeting with Mr Corbyn he asked him three times whether he is prepared to see a split but “he offered no answer”, while the leader’s ally and shadow chancellor John McDonnell “shrugged his shoulders and said ‘if that’s what it takes’”.
Mr Smith said: “I am not prepared to stand by and see our party split.”
Mr McDonnell said Mr Smith’s claim was “complete rubbish”, while Mr Corbyn told BBC Radio 4’s The World This Weekend he would be happy to meet Mr Smith and said: “I’m not splitting anything.”
The leader and his allies have insisted the Labour rulebook means he will automatically be on the ballot and any challenger will have to secure the names of 51 MPs - 20% of the party’s parliamentarians in Westminster and Brussels - to be nominated.
But opponents have interpreted the document to mean that Mr Corbyn will also require the support of MPs to stand - something which is unlikely to happen.
If Mr Corbyn is automatically on the ballot, the support in the party’s grassroots which swept him to victory in 2015 could do so again - leaving his opponents facing an even deeper problem.
The party’s National Executive Committee (NEC) will decide on the rules after a contest is formally triggered.
Ms Eagle said the rules are not clear on whether Mr Corbyn should be on the ballot, but told BBC One’s Sunday Politics: “Anyone who aspires to lead the parliamentary party who cannot get 51 members, 20% of the parliamentary party, to back them is not going to be able to do the job properly.”
On BBC One’s Andrew Marr Show, Mr Corbyn said he would be prepared to go to court if the NEC ruled he would not automatically be on the leadership ballot.
“I will challenge that if that is the view they take,” he said.