Work was due to start last summer on the junction 7A project to the north-east of Harlow new town, and associated link roads to join the B183 Gilden Way.
Now Essex County Council has confirmed widening of Gilden Way will start in late spring, with works on the motorway junction and link road likely to start in the autumn.
The new junction is planned to open in 2022.
Graham will now finish detailed design work with its design partner Aecom.
Funded through Highways England, the Department for Transport, Essex County Council and the South East Local Enterprise Partnership, the £40m scheme is located between Junctions 7 and 8 of the M11.
On the award of the contract, Stephen Hand, Pre-Construction Director of the GRAHAM Civil Engineering division, said: “We’re pleased to have been awarded this hugely beneficial highways scheme by Essex County Council which is the latest in our growing portfolio of highway improvement schemes. ”
Cllr Kevin Bentley, Deputy Leader of Essex County Council and Cabinet Member for Infrastructure, said: “This is a critically important piece of new infrastructure which we have been working with partners for a number of years to help make a reality.”