The deputy First Min-ister said the change will save around £70 a year for an average household bill.
She said the levy on fuel bills from West-minster pays for energy efficiency schemes, raising £120million a year.
She added: "An SNP government in an independent Scotland will remove the cost of energy saving measures and the warm home discount from energy bills.
"We will provide that funding from central government resources. That will mean direct government funding for fuel poverty schemes of at least £200m per year.
"That money will be spent in a fully joined up way, on schemes designed in Scotland to meet Scottish circumstances."
She said the Scottish Government already contributes £80m to energy efficiency programmes.
Ms Sturgeon told the SNP conference in Perth the move would save 5% on household energy bills.
She added it would be "a real and lasting cut" in energy bills.
Finance Secretary John Swinney said an independent Scotland would treat young job-seekers better than Westminster does. He branded welfare reforms and the UK Government's Work Programme a failure.
He said: "Where our apprenticeship programme has a success rate of over two thirds, the Work Programme sends two-thirds of people back to the job centre.