Last month Finance Secretary John Swinney, announced a £20million top-up for councils to pay out in discretionary housing payments for the current financial year.
Today, the Deputy First Minister announced the same amount will be made available next year as well.
Mr Swinney said previously when asked why the cash was not available for the next year that he didn't want to let Westminster "off the hook", provoking accusations from Labour he was leaving tenants "on the hook".
Speaking at the SNP Conference in Perth, Ms Sturgeon will say: "Last month, we announced an extra £20m in this financial year to help those affected by the bedroom tax.
"That money is enabling councils to top up their discretionary housing payments to the maximum amount that Westminster legislation allows.
"I can announce today that we will allocate up to £20m again next year so that we can continue this vital help for those hit by the bedroom tax."
She repeated her call that independence would allow Scotland to reverse the worst of the welfare cuts. She said: "I promise that we will continue to do all we can to help, but only an independent Scottish Parliament will give us the powers we need to scrap the bedroom tax."
Alex Salmond opened the conference yesterday and said people will choose trust over fear in the independence referendum next year.
The First Minister said no one now doubted the ability of Scotland to be a successful independent country.
He said: "People trust the Scottish Government to act in the best interests of the Scottish people."
He said this represented a "natural majority" for independence.
Opening the four-day conference, in front of several hundred delegates, Mr Salmond said the No to independence campaign, Better Together, christened themselves 'Project Fear'.
And he quoted former Scottish Secretary, Michael Moore, who said he found it offensive when it was suggested Scotland would not be capable of independence.
He said: "When even the most bitter opponents of Scottish independence agree that Scotland has got what it takes, then it is clear that the only thing people have to fear is Project Fear itself.
"The real debate, the central question people will answer in next year's referendum, is who can be trusted to make the best decisions for Scotland."