Before a final vote at Holyrood last night, the Finance Secretary confirmed £50 million would be available from April to offset housing benefit cuts known as the bedroom tax, which have been imposed on 76,000 households in Scotland.
The cash includes £15m from the UK Government and £23m from the Scottish Government to be paid direct to tenants as "discretionary housing payments" or DHPs.
A further £12m will be used to write off rent arrears if the Department for Work and Pensions refuses to allow it to be spent on DHPs.
The move, which effectively abolishes the bedroom tax in Scotland from April, paved the way for Labour to support Mr Swinney's spending 2014/15 plans - the first time the party has voted in favour of a budget since the SNP took power in 2007.
The LibDems backed plans to offer free childcare to more two-year olds from disadvantaged families, while the Greens welcomed measure to promote healthy eating and active lifestyles.
The Conservatives refused to support the budget, accusing Mr Swinney of using it for "political posturing".
Graeme Brown, the director of Shelter Scotland, said: "Ultimately the only way to banish the bedroom tax for good is to scrap the policy. Until that is possible, these moves to help those affected should be seen not only as a victory for common sense, but also for social justice."