The scheme is being funded through the council’s successful bid to the UK Government’s Housing Infrastructure Fund for £249m.
The council was forced to rethink procurement plans for the project last year in the face of volatile market costs.
Council procurement chiefs had originally planned to select a contractor in July 2022.
Instead, procurement chiefs rescoped the procurement plan to include the new simplified approach to early contractor involvement and amendments to allow for rising construction costs.
If planning is approved, Galliford Try will build a new slip road onto the M5 southbound and a new slip road off the M5 northbound to create an all-movements signalised junction.
The new junction will provide access in all directions, unlocking housing and employment opportunities at sites proposed for development including west and north-west Cheltenham.
The scheme also includes a new link road connecting the A4019 to the B4634 in west Cheltenham and widening of the A4019 Tewkesbury Road.
David Lowery, managing director of Galliford Try’s Highways Business, said: “This opportunity truly plays to our strengths to work collaboratively in integrated project teams to drive value early in the process and ensure the project delivers on its strategic outcomes.”