Under the new job support scheme, which replaces furlough, the government has pledged to pay up to £697.92 for employees working fewer than their normal hours.
Employers will continue to pay staff for the hours they work, which will then be topped up for those hours not worked.
The government and the employer will each pay a third of their equivalent salary and employees must be working at least 33 per cent of their usual hours.
Cllr Whitehead said: "We are pleased the government has listened to calls to extend help for businesses affected by coronavirus over the winter months.
“These new measures will go some way to reassure businesses that support will be available to help them and their staff through these challenging times.
"We will consider the full guidance of these schemes when available and will feedback any issues or concerns we have direct with government to ensure we can protect Wiltshire's jobs, businesses and economy.
"We are committed to doing all we can to support businesses in the county and would encourage any business concerned about the impact Covid-19 is having on their livelihood to contact us as soon as possible for help and advice."
Outlining these plans, the chancellor of the exchequer said: “The resurgence of the virus and the measures we need to take in response, pose a threat to our fragile economic recovery…
“Our approach to the next phase of support must be different to that which came before.
“The primary goal of our economic policy remains unchanged – to support people’s jobs – but the way we achieve that must evolve.”
The scheme will come into effect from November 1 and will last for six months.