Main refurbishment work will take until December with the car park and servicing area set to finish in 2014.
Indoor market traders in the non-food section will be relocated temporarily to the current outdoor market during February.
The market’s fruit and veg section and the fish market will be open for business as usual.
Leader of Bolton Council, Councillor Cliff Morris, said: “We are delighted to have appointed Willmott Dixon to redevelop Bolton Market as they have a long and successful track record with retail and refurbishment projects like this.
“They have worked on many retail projects in the North West which have required the sites to be remodelled similar to what we’re doing in Bolton.”
The design team for the project is led by architects Davis Wetherill Partnerships who have recently completed the refurbishment of the Grade II listed Accrington Market Hall for Lancashire County Council.
Managing director for Willmott Dixon in the North West, Anthony Dillon, said: “We are delighted to be working with Bolton Council and the Davis Wetherill Partnership in delivering what will be significant improvements to such an important and historic market.
“We will be working closely with Bolton Council to ensure we maximize the local economic benefit through engagement with local subcontractors, suppliers, and the employment of local labour.”