Initially, Carillion will advise on how to best to carry out a £10 million programme of extensive concrete repairs to the roof and walls of both tunnel bores.
The Council says the Woodhouse Tunnel is suffering severe concrete damage and deterioration as a result of prolonged, extensive chloride ingress from winter de-icing salts.
The damage is so severe that the structural capacity of components is now being affected.
The tunnel needs extensive concrete repairs to the roof and walls of both tunnel bores and strengthening for vehicle impact loading to the area of the tunnel supporting the Leeds General Infirmary buildings.
Strengthening work for vehicle impact loading and protection to the rest of the tunnel will be also required.