A Bill to be unveiled by new Work and Pensions Secretary Yvette Cooper will set out how the target will be measured alongside moves to force governments to monitor progress.
Ms Cooper conceded that meeting the deadline, originally set by Tony Blair in 2000, remained "a big challenge", with an interim target to halve it by next year already looking almost certain to be missed.
But she said Labour would not shy away from the issue and wanted to lock future administrations into efforts to ensure no youngsters were "left behind" in future.
The legislation will include targets to have fewer than 10 per cent of children living in households with less than 60 per cent of median income and fewer than 5 per cent in those with less than 70 per cent.
It will also promise an absolute family income below which no more than 5 per cent of youngsters will be living and a maximum proportion - yet to be set - for those living in relative poverty for three out of four years.
Ministers will be required to publish a three-yearly strategy and annual progress reports and an advisory child poverty commission will be set up.
Duties will also be placed on local authorities and other "local delivery partners" to assess local needs, produce strategies and consider the issue in developing Sustainable Communities Strategies.
"This Bill is about giving every child a fair chance in life," Ms Cooper said.
"I want a society where children don't miss out on school trips, aren't stuck in poor housing with no space to do their homework and aren't left behind because they don't have a computer or internet access.
"This is a big challenge, and one which we will not shy away from. It is about the society we want to live in. It holds current and future government's feet to the flames and won't allow any government to quietly forget about child poverty or walk away.
"It sets out what we need to do from a national to a local level to work together in communities across the country to end child poverty by 2020."
End Child Poverty director Hilary Fisher said: "With four million children in poverty in the UK today it is important the Government focus on the real challenges facing children living in poverty.
"We welcome the Child Poverty Bill as an important step forward in making tackling child poverty a priority for all governments - ending child poverty is not a luxury, but a necessity.
"It will be particularly important to be clear how government will be held to account in the legislation.
"We believe the first step to tackling child poverty in the future is tackling it today. We need to see urgent action to help hard-pressed families now as well as a strong Bill which carries forward that action into the future."
The Department for Work and Pensions said getting parents into work would be key to success.
Shadow work and pensions secretary Theresa May said: "Gordon Brown's pledge to halve child poverty by 2010 is just one of countless Labour promises that lies in tatters.
"It is a tragedy that the number of children falling into the poverty cycle is continuing to rise.
"The Government needs to wake up and get a grip of this problem.
"Simply relying on means-tested benefits to address the symptoms of poverty is unsustainable. Instead we must tackle the root causes of poverty, such as educational failure, family breakdown, drug abuse, indebtedness and crime."
Ms Cooper said 500,000 children had been lifted out of poverty since Labour came to power in 1997 and measures already in place would double that figure.
"It beggars belief that the Tories can criticise this Government's determination to eradicate child poverty. In 18 years in power, the Tories doubled child poverty and turned their backs on the unemployed.
"Now they would do so again by opposing Labour's help for unemployed parents and with their plans for 10 per cent cuts in education and children's services."
Theresa May said politicians should be tackling the root causes of child poverty, including family breakdown, unemployment and educational failure.
She told BBC News: "Putting a bill sets a commitment, it raises the profile of the issue but what actually matters is what we do to help people."
Asked if she would support the Bill, she said she had not yet seen it but added: "We are supportive of the commitment that the Government has given on child poverty."
Ms Cooper said: "A recession does obviously make it harder to make progress. The big thing over the next few years is preventing parents getting stuck in long term unemployment."
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