Work and Pensions Secretary James Purnell is proposing an amendment to the Pension Bill enabling people to buy up to an extra six years of National Insurance contributions.
Each extra year of National Insurance contributions adds around £160 a year to the state pension that people are entitled to.
But the Government is increasing the cost of buying extra years from its current level of £420 per year to ensure the move will not cost it anything, although it has not yet said what the increase will be.
The new top-up scheme is available only to people who already have at least 20 years of National Insurance contributions, meaning that many women could still miss out.
It also applies only to people who reach the state pension age between 6 April 2008 and 5 April 2015, so will not enable the majority of women who have already retired to boost their pension.
The Government estimates that around 550,000 people will be eligible to buy up the extra years, but in reality it expects only around 20 per cent of these to take advantage of the scheme.
The announcement applies to both women and men, although women are thought to make up 90 per cent of those who will benefit as they are far more likely to have a broken contribution record as a result of taking time off to look after children or elderly relatives.
People can already buy six additional extra NI contribution years, but there are time limits on when these years can be purchased.
Under the new scheme people will be able to buy any six years going back to 1975, meaning they will now be able to buy up to 12 extra years.
The measure is the latest part of the Government's reform programme which aims to make the state pension fairer for women.
Other moves include introducing National Insurance credits for carers and reducing the number of years of NI contributions people need to qualify for the full basic state pension from 44 for men and 39 for women to 30 years for both sexes from April 2010.
One of the reasons the Government gave for raising the cost of buying extra years is that each year now represents a higher proportion of the state pension.
Only around a third of women reaching pension age currently qualify for a full basic state pension.
Today's announcement marks a change of heart for the Government which last year overturned an amendment to the Pensions Bill designed to give people the opportunity to buy back extra years of missed contributions.
Mr Purnell said: "Since 1997 we have reduced absolute pensioner poverty by 1.9 million and our radical reforms of the state pension have made it fairer, more generous and more widely available.
"By 2010 around 75 per cent of women reaching state pension age will be entitled to a full basic state pension, rising to over 90 per cent by 2025, compared to around 35 per cent today.
"However, we are mindful of the potential disadvantages faced by those who do not have a full work history, mostly women and those with caring responsibilities."
He also praised Baroness Hollis of Heigham, who has tried several times to amend the law to allow women to make top-up payments.
Pensions campaigner Ros Altmann said: "This doesn't really apply to women who have already retired, so they will continue to miss out."
She urged other people who were considering buying the extra years to take advice first.
Single pensioners who have no other source of income already qualify for the Pension Credit, which is £130 a week, meaning they would not benefit by buying the extra years.
Liberal Democrat work and pensions spokeswoman Jenny Willott said: "The Government's change of heart on women's pensions is welcome, but it is disappointing that it is so stingy.
"Women who saw the news this morning will be bitterly disappointed when they read the small print of this announcement. These changes will not benefit those women who are the worst off and facing the bleakest retirement."
The move was also criticised by the National Pensioners Convention (NPC), which said it was nothing more than "window dressing".
NPC vice president Dot Gibson said: "Up to five million existing women pensioners fail to get a full state pension because they spent years raising children, caring for relatives or working part-time."
But other groups welcomed the announcement.
Gordon Lishman, director general of Age Concern, said: "We are absolutely delighted by this decision, which will give thousands of older women the opportunity to build up a better state pension.
"Today's announcement is a victory for a generation of women who have been ignored by previous pensions reforms.
"We have long campaigned for this amendment to the Pensions Bill and we are thrilled that the Prime Minister's recent pledge to deliver a fair pensions deal for women is being honoured."
Mervyn Kohler, special adviser for Help the Aged, said: "This is a welcome step - in particular, it could benefit a number of women who have a rather incomplete employment history because of time they have spent as mothers or carers.
"Although the state pension is not generous, a full pension is better than the reduced pension which many women retiring now are receiving."
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