As many as 1.9 million working families will get the chance to benefit from a childcare subsidy worth up to £2,000 per child under government plans.
The online scheme, affecting children up to the age of 12, will come in from September next year.
David Cameron said "squeezed" families would benefit and Nick Clegg added it would be "really simple" to use.
But Labour said the assistance - announced ahead of Wednesday's Budget - would be "too little, too late".
The parties are making rival offers to help families deal with the cost of childcare, which the opposition says has risen by 30% since 2010.
The Family Childcare Trust says the average weekly cost for 25 hours of care for a child under the age of two is £109.89.
At the moment, employees of participating companies can reduce their childcare costs through a tax-free voucher scheme. But only about 5% of UK employers and 450,000 families are signed up to it.
Ministers say the new scheme - which will come into force after the 2015 general election - will mean twice as many parents are eligible for support, including the self-employed.
When it was originally announced a year ago, the government said the maximum support available would be £1,200 per child and that it would be open to families where both parents work and earn less than £150,000 a year.
It also said the scheme would be phased in over seven years.
Following a public consultation, ministers have agreed to increase the value of the scheme to a maximum of £2,000 per child, and accelerate its implementation, extending it to all under-12s within the first year.
Parents will have to set up an online account, allowing them to get a 20% rebate, per child, on the annual cost of childcare of up to £10,000 a year.
For instance, if their annual childcare bill was £6,000, they would pay £4,800 into the account with the government adding £1,200.
Anyone working part-time and earning more than £50 a week, parents on maternity, paternity and adoption leave and those starting their own business will all qualify.
The prime minister and his deputy promoted the scheme on a visit to a London nursery.
Mr Cameron said: "This is about helping all families, but particularly those families that do feel their finances are squeezed,
"I want to give families greater stability, greater peace of mind, greater security. And obviously being able to have £2,000 tax relief per child is going to be a huge help to millions of families across Britain."
Mr Clegg said introducing different income cut-off points - rather than an earnings ceiling of £150,000 per parent - would have made it too complicated.
"This is really simple," he said, adding: "For every 80p you pay, the government will pay 20p. It's as simple as that."
Critics have complained that homes where one parent stays at home to look after children will not benefit.
Mr Clegg said: "This scheme is aimed at parents who are both at work."
He added that the coalition's decision to raise the point at which people start paying income tax to £10,000 a year would also help many households.
Labour claimed the proposal was "unravelling". Shadow children's minister Lucy Powell told the BBC: "What the government have announced today is £750m which they say will be shared between £1.9m families - I work that out to be around £400 a year for the average family. So they are making this sound a little bit more attractive than it actually is."
But Treasury minister Nicky Morgan told BBC Radio 4's World at One there was no "average family" and insisted that up to £2,000 per child would be available, adding: "The point about the scheme is it is simple and flexible."
Under the government's proposals, the current Employer Supported Childcare scheme will continue but will not be open to new members from August 2015. Existing participants will be able to transfer to the new scheme but will not be able to take advantage of both.
The Conservatives, Liberal Democrats and Labour are all seeking to promote family-friendly policies in the run-up to next year's election.
The government has increased the entitlement for three- and four-year-olds to free early years schooling from 12.5 to 15 hours a week while Labour has said this will go up to 25 hours if it wins power after 2015.
Labour warned that parents were likely to be paying more of their disposable income towards childcare in 2018 than they are now as a result of the government's policies.
"Of course any childcare support is welcome but this government has done nothing in this Parliament to help parents experiencing a cost-of-living crisis," said Labour's Lucy Powell.
"[Prime Minister] David Cameron has cut support for children and families by £15bn since he came to office, And today he confirms that no help will arrive until after the election. This is too little, too late."
Children's Society chief executive Matthew Reed said the government's scheme would make a "huge difference", but added: "While this move is extremely welcome, it is critical these families truly benefit from it. Greater assistance for these families must be the focus of tomorrow's Budget... This must not be a case of giving with one hand and taking with the other."