The firm will deliver three roundabouts worth around £7m for the project and enter into an early contractor involvement deal for the £80m contract to deliver 7.5km of dual carriageway.
It is understood that Leeds City Council separated Carillion from bid rival Balfour Beatty as Carillion had opted for self-delivery on the roundabout work.
It is the second project to be secured by the contractor from the council following the award of the £7m cycleway.
The ELOR will stretch from the Outer Ring Road at Red Hall round the east side of Leeds to Thorpe Park joining a new Manston Lane Link Road where it would connect into the existing highway infrastructure and link to the M1 motorway.
The project is broken down into three phases: A6120 Outer Ring Road – Advance Junction Improvements; main ELOR works: and A6120 Outer Ring Road Improvements/Enhancements
Construction is expected to start in Spring 2018 with completion by the end of 2021.
The project is being funded by the West Yorkshire Plus Transport Fund and developers.