The Wolverhampton-based firm is expected to start work early next year on the project which involves the design and build for the reconstruction and widening of the westbound A45 South Bridge.
The news follows the announcement last month that the Department for Transport was backing the scheme to the tune of £8.3 million.
The current bridge, which dates back to the 1830s, is used by 30,000 vehicles a day and serves as an important transport link to the many businesses in and around the area, including the NEC, Jaguar Land Rover and Birmingham Airport.
But it is narrow and no longer ideal for current usage so will be replaced with a new bridge with increased lane widths and an additional lane.
There will also be safe pedestrian access along the A45 towards the airport and improvements to the slip road.
Between January and December 2015, Carillion will construct an accommodation bridge alongside the existing bridge to allow for the route to remain open throughout.
Demolition of the old bridge structure will take place over Christmas 2015, with an expected completion date of August 2016 for the new bridge structure.
Mansfield-based North Midland Construction, on behalf of Birmingham Airport, is currently carrying out widening works on the A45 on both sides of the South Bridge ahead of its reconstruction.
These works are due to be completed in November 2014.
Mark Davies, managing director of Carillion Civil Engineering, said: "The work takes place on a vitally important transport link in Solihull and we will work hard to minimise the impact of the work on local stakeholders and the travelling public."