Interserve was originally on the job buts its £9m contract was terminated last April following a disagreement over costs.
The total project will now cost £20.2m with construction work expected to come in at £16.5m.
Recent surveys have revealed significant structural problems with the tower on the north side of the site, which is currently subsiding and cracking.
The main roofs are also in need of replacement to prevent further water ingress.
Construction will see the building stabilised through major underpinning, protected from water damage and given a new lease of life.
The Guildhall is expected to reopen in Spring 2021.
Councillor Nigel Ayre, Executive Member for Finance and Performance, said: “This is the first significant investment in our Guildhall for 60 years and this extensive restoration will protect the buildings for another 50-60 years.”
Chris Winspear, Construction Director at Vinci Construction UK, said: “We are very much looking forward to starting construction works and delivering a building that we can all be extremely proud of.
“It’s an exciting opportunity which will greatly benefit the community and residents of York”.