All babies will receive at least £250 at birth - and poorer children up to £500 - with the money invested until they become adults.
'Baby Bond'
Birth: £250-500
Age 5: £50-100
Age 11: £50-100
Age 16: £50-100
______________
Total: £400-800
Mr Blair said: "Piece by piece we are dismantling the barriers that hold people back from developing their potential to the full."
Shadow chancellor Michael Portillo dismissed the scheme as a "con" timed purely for the expected June election.
In addition to the payments at birth, poorest children will have top-ups of £100 on their fifth, 11th and 16th birthdays - better off children will get half that amount.
Trust fund
The money - up to £800 in all - would be invested in a trust fund, potentially yielding thousands of pounds by the time a child reaches adulthood.
Mr Blair also announced a Savings Gateway Account under which money invested by poorer households would be matched pound for pound by the Treasury.
Mr Blair told a Downing Street press conference on Thursday the bonds would help create a "real land of opportunity for all".
He said: "We want to see all children growing up knowing they have a financial stake in their communities.
"It will be a financial springboard to better education, better homes and a better life."
Cash for education
Earlier Chancellor Gordon Brown said there would be consultation on the age at which children would receive the money and under what conditions.
Ministers would like it to be spent on education, training, buying a home or setting up a business.
Mr Portillo told the BBC: "It's a complete con.
"What he plans to drip feed to the next generation is tiny compared to the amount he has taken from this generation, from families, pensioners and businesses.
"Labour's stealth taxes are impoverishing Britain, soaking up disposable income and punishing saving."
Adult savers
Under the Savings Gateway Account, the government would match savings of poorer adults pound for pound up to £1,800.
They would have to save for three years and after that the money could be transferred to an individual savings account (ISA), a pension or a children's trust fund.
The idea is based on schemes in the United States set up by the former President Bill Clinton.
In America low-paid savers with individual development accounts get two tax dollars for every dollar they put away.
On average people in the schemes are saving $25 a month.
The government clearly sees this as one of the big ideas for the election.
There are 16 million people in the UK with no savings at all - most of them on low incomes.
In a phrase reminiscent of Margaret Thatcher, Mr Brown says this will open up "a wealth-owning, asset-owning democracy for all".
'Gimmick'
Liberal Democrat leader Charles Kennedy said there was "gimmickry" in the pre-election timing of the bonds.
He added: "For many of those who in 18 years time will go on to be university students, all it will do is provide a dent in the overhang generated by student tuition fees."
If the £800 per child's trust fund had been invested on the stock market 18 years ago, it would be worth around £4,500 today.
But an independent financial adviser consulted by the BBC warned that future investments could yield much less.