The contract was re-tendered in March after the council rejected Wates’ budget of nearly £5m.
Tomlinson said it can carry-out the construction work for £3.6m.
Councillor John Burrows, Leader of Chesterfield Borough Council said: “We are pleased to be working with G F Tomlinson as our construction partner. They are a local firm, with an excellent track record and have come in with a very competitive price.
“It was unfortunate that we had to re-tender the contract, as it has delayed the scheme, but it has saved nearly £1.4 million, so there’s no question that it was the right decision to make.
“The new tender isn’t at the expense of the quality of the scheme and the original planned design still remains.
“By employing a local firm we’ll also have more opportunities to subcontract with local suppliers and companies, giving local people employment throughout the construction phase.”
Work on the Market Hall is due to start on site in September 2012, with a completion date of early September 2013.
Stuart Lawrence, Managing Director of G F Tomlinson said: “As a local Derbyshire contractor, we are very committed to giving something back to the communities we work in.
“Therefore we always adopt a ‘think local’ policy on procurement and will be inviting local suppliers and subcontractors to quote for works on this project.
“This will provide a boost to the local economy by generating local employment opportunities and recycling the ‘Chesterfield’ pound.”
Andy Hands, Business Manager for Wates Construction, Midlands, said in March: “We have worked hard with Chesterfield Borough Council to try and bring this project in line with the council’s financial limitations.
“In times of austerity we appreciate the need for tight financial planning, but we were unable to feasibly deliver the project within the budget.
“It is with regret that we will not be delivering Chesterfield Market Hall and we look forward to working with the council in the future.”