The Scottish Government revealed the city would get the largest share of a £20m bail out announced last month by Finance Secretary John Swinney in his Scottish budget.
The cash takes the money available to Glasgow City Council to distribute in Discretionary Housing Payments (DHP) to £6.4m.
The Westminster Department of Work and Pensions gave an initial allocation of £2.9m to help social tenants affected by the benefit cut.
The council said the cash was not enough and the level of demand in the city would require around £10m to help all tenants affected.
Today the Scottish Government revealed the share of the £20m across the country.
Glasgow receives £3,553,117.
The Scottish Government said it takes the money available across Scotland for the payments from £15m to £35m.
Margaret Burgess, Housing Minister said: "We are determined to do everything we can to help mitigate welfare cuts, including the bedroom tax and this funding will make a real difference.
"We also recognise the huge financial pressures that have been placed upon authorities by welfare reform, this is why we have made available an additional £20m to be distributed across every local authority.
"This is the maximum permitted under UK legislation and ensures that far more people can access the financial support they need."
Housing charity Shelter Scotland, who called for the cash before the Budget, said while it still won't help everyone affected it would help many more than before.
Graeme Brown, Director of Shelter Scotland, said: "It means that local authorities can now offer a lifeline to thousands more households struggling to pay their rent as a direct result of the iniquitous bedroom tax."
Opposition councillors in Glasgow have called on the city council to also put in cash to ensure everyone affected is able to receive help.
Deputy SNP Group leader, Billy McAllister said: "I have been calling for the Council to do its part since March 2013, with Labour turning the other cheek consistently over the past six months.
"Instead of taking action themselves, they have waited until the Scottish Government stepped in."
A Glasgow City council spokesman said the council had been campaigning to ensure the city received a fair share of funding from the Scottish Government and from Westminster to allow it to help citizens affected by UK welfare reforms