It is the final hurdle for the long-awaited project, which will link Dudley with Birmingham, Wolverhampton and the national rail network.
Originally the line was expected to cost £370m including around £60m worth of contingency, but after investigation work this is £80m higher at £450m
The Midlands Metro Alliance, which includes civils contractors Colas, Barhale and Bouygues UK, will start work in the autumn.
The Wednesbury to Brierley Hill route extension, running largely along a disused heavy rail corridor, is projected to trigger 2,000 new homes a year, almost one million square feet of commercial space
An expected increase in the number of people paying council tax from the extra new homes that could be built would bring in an estimated £580m.
Councillor Qadar Zada, leader of Dudley Council, said: “There’s no doubt this is a trailblazer project which will have a massive impact on the borough, beyond transportation. It will be the catalyst for new homes, commercial opportunities, jobs and much more for this borough.
“It’s taken a long time to get to this point, but the funding makes this scheme a reality and I am very much looking forward to seeing work start in Dudley as soon as possible.”
Once up and running there will be up to 17 new stops along the 11 kilometres of track. The new system will also reduce journey times by half compared to travelling by bus.