He said an extra £15 million would be used to help tenants struggling to pay their rent even if the UK Government refused to relax rules limiting the amount of compensation they can receive directly.
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The move means £50m in total will now be made available in the new financial year, the amount required to completely cancel out housing benefit cuts known as the "bedroom tax" for all 76,000 Scots households affected.
Mr Swinney's announcement came ahead of a final vote on the 2014/15 Scottish budget at Holyrood today.
He again called on the UK Government to allow the extra funds to be used for "discretionary housing payments", or DHPs, insisting it was the best way to compensate tenants who have lost benefit.
But he said the money would be available "in all circumstances".
The announcement marks a climbdown for Mr Swinney who originally refused to help tenants on the grounds he did not want to "let the Westminster Government off the hook" over the issue of the bedroom tax.
He later argued it was illegal for the Scottish Government to provide more than £20m support under the rules covering DHPs.
The move paves the way for Labour to vote for an SNP budget for the first time since the Nationalists took power in 2007.
Mr Swinney said: "Parliament has the chance to come together and confirm that it rejects Westminster's 'Bedroom Tax' - a tax which was imposed on Scotland despite 90 per cent of Scotland's MPs voting against it."
The Scottish Government U-turn came after UK ministers said the bedroom tax could be scrapped without their persmission.