Preparation work is expected to get under way in the autumn with main construction beginning in January.
Work is due to be completed by summer 2022 to increase capacity at the traffic bottleneck and improve safety.
The scheme is a joint venture between Highways England and Walsall Council, supported by the Black Country Local Enterprise Partnership.
The current junction is over 50 years old and replacing the bridges which carry it over the motorway will avoid the need for extensive maintenance.
Highways England Project Manager David Reed said: “We are delighted to announce that John Sisk & Son have been appointed to lead this important scheme which will tackle congestion at a very busy junction at the heart of the country.
“This is a significant milestone for the project which will ultimately bring smoother and safer journeys for the many thousands of drivers using junction 10 every day.”
Paul Brown, Managing Director UK Civils, John Sisk & Son, added: “The project provides us with an opportunity to further enhance our reputation and continue our excellent relationship with Highways England, following the recent successful completion of the A19 works in the North East.
“We are committed to delivering the project in line with Highways England’s key imperatives and to maximising social value to benefit Walsall Council.