Chiefs at Wolverhampton Council said the move would allow Willmott Dixon Interiors to "push forward" with the revamp.
Work had been carried out by the contractors following Shaylor's collapse last year through a pre-construction agreement.
Now a full contract is set to be signed off "imminently" after it was handed the green light by council chiefs.
Councillor Ian Brookfield, leader of Wolverhampton Council, said: "Covid-19 has had an unprecedented and unavoidable impact on major construction projects nationally and internationally.
"After being hit hard by Covid, regeneration projects like the Civic Halls are even more important to our economic recovery.
"We are creating a truly outstanding entertainment venue, in the heart of the city centre, which will bring in millions of pounds to our local economy and safeguard hundreds of jobs.
"This will be vital to our future. Since appointing Willmott Dixon Interiors as our preferred contractor, they have made excellent progress under a pre-construction service delivery agreement to keep the refurbishment and improvement works on schedule and on budget.
"The imminent signing of the full contract will see Willmott Dixon Interiors push forward this exciting redevelopment through to the opening of what will be a venue that my fellow Wulfrunians will be quite rightly proud of.
"At the moment site works are temporarily paused until it is safe to recommence operations in line with the Government’s Covid-19 health and safety guidelines, which we envisage being in the coming weeks."
Claire Nye, director of finance at Wolverhampton Council, said the current budget remained sufficient for the project.
She told a meeting at the audit and risk committee: "The contract is of a value that's in the original budget allowing for the contingency, so it's still within the £38.1 million budget.
"However, there are new risks that we have worked with our advisors to understand, specifically in relation to Covid.
"Before Covid the budget was sufficient and the contract is within that value – but because of Covid we have to assess those risks and make allowance for that because it would be inprudent to proceed without doing so clearly."
Wolverhampton Council's cabinet members scrutinised the risks – and the potential value of those risks – at a meeting on Tuesday, where they approved the go-ahead.
Discussions will now be held by legal experts to formalise the contract been Wolverhampton Council and Willmott Dixon Interiors.