From October they will again become eligible for a one-off grant to ease the strain of buying equipment such as prams even if they have other children.
Until last year less-well- off parents were able to claim £500 after having a baby, no matter how many children they already had.
However, Coalition ministers changed the system to limit the grants to just the first child in a family.
The Department for Work and Pensions (DWP) said the Government had to work within limited resources and that families should be able to re-use equipment bought for a first child.
However, campaigners and politicians complained that parents who had had multiple births were being discriminated against and could not be expected to use a single buggy for two or more babies.
After a long campaign, ministers have now agreed and new parents of multiple births will again become eligible for the payments.
The move has been welcomed by the Twins and Multiple Births Association (Tamba), who estimate that 2000 to 3000 couples every year across the UK will now get extra funds, around 200 or so in Scotland.
Tom Greatrex, the Labour MP for Rutherglen and Hamilton West, who has campaigned on this issue, said: "This is a welcome change of heart from the UK Government, and will have a significant impact on low-income Scottish families with twins or triplets at a time when household incomes are being squeezed."
Mr Greatrex's MP's salary means he would not have been eligible for the grant himself, but he said that as a father of twins he understood the impact of a multiple birth.
"I know that having twins is a rewarding privilege, but it can be very expensive.
"For families on low incomes, the grant is a much-needed support to meet the costs of a new baby – but it was crazy that it was not available for multiple births following a single birth."
Keith Reed, chief executive of the Tamba, said: "We are really delighted the Govern-ment has recognised the additional financial needs of multiple-birth families when setting up home for their newborns.
"We have been receiving calls for families who can't afford to meet their babies' basic needs and this change will make a significant difference."
A spokesman for the DWP said: "We will pay Sure Start maternity grants to parents with a child under 16 and a subsequent multiple birth."
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