The new bridge over the railway line will be a permanent replacement for the former Jumble Lane level crossing, which was closed to improve safety in the area.
NMCN had previously been identified as the preferred contractor but fell into administration within days of the initial contract being signed.
Keltbray will now build the bridge off-site in several weeks’ time, while on-site work will start in July before the structure is opened next summer, according to Barnsley Council.
Network Rail pledged £2m towards the cost, with the South Yorkshire Mayoral Combined Authority contributing a further £4.8m via their Get Britain Building and Transforming Cities funds, with the remaining cash being put up by the council.
Coun Tim Cheetham, cabinet spokesperson for regeneration and culture, said: “The process of appointing an alternative bridge contractor for the Market Gate bridge has been quite complex.
“Our procurement and project teams have been working extremely hard on this for the past few months following the administration of NMCN.
“I’m delighted that we’re able to update everyone with this excellent news that we’re now able to press ahead and complete this important part of our town centre regeneration.
“The bridge will be an iconic addition to our fantastic new town centre and the first thing people will see when arriving by bus or train.
“It will bring people from the transport interchange directly into our new Glass Works square and it will be an impressive addition to the skyline.”
The £9.7m overall cost - almost double the original estimate - includes professional fees and sewer diversion work, as well as further public realm and highway improvements at both ends of the bridge.
South Yorkshire Mayor and Barnsley Central MP Dan Jarvis added: “It’s very welcome to see that work is getting underway on Barnsley’s new Market Gate pedestrian bridge.
“This regeneration project will not only support the wider transformation of the town centre, it will also unlock significant investment opportunities for Barnsley on adjacent development sites.
“Once complete, the project will massively improve the town centre’s public realm, create beautiful green spaces, and enable people to swap the car for walking and cycling.
“Above all, it will mean a permanent link from the town centre to Oakwell on matchdays which I know will be heartily welcomed by fans and Barnsley FC.”
The leader of Barnsley’s Liberal Democrat group - Coun Hannah Kitching - said the project has ‘become a joke’ due to the spiralling costs.
“The council has been hell-bent on pursuing this,” she said.
“There’s always cuts for residents, cuts in services, increasing bills, but there’s always money for a town centre vanity project.”