Bosses at the Dudley attraction have given the green light to the Forging Ahead project, which will see 22 new historic buildings added to the site – including the brick-by-brick relocation of Holly Hall's Woodside Library.
The expansion – the biggest since the museum opened in 1978 – will focus on the period from the 1940s to the 1960s, and will feature an NHS clinic, a barbers, and a Co-op supermarket.
The old Stanton's Music Shop from Castle Street, Dudley, will be reborn, and there will also be a recreation of the Elephant & Castle pub, which once dominated the corner of Stafford Street and Cannock Road in Wolverhampton.
A new industrial quarter will sit alongside the new town, while a new visitor centre will also be built.
Work had been due to start last year but was delayed due to the pandemic. The site is currently home to a vaccination centre.
Contractor Balfour Beatty is set to start work before the end of this month after the museum was awarded £3.74 million from the latest round of the Government's Cultural Recovery Fund.
Councillor Patrick Harley, leader of Dudley Council, said: "This is fantastic news and a really exciting new development for what is already a top-class visitor attraction.
"It’s been well documented that the pandemic and lockdowns have hit our tourist attractions hard, but its great to see one of the biggest outlining plans to come out the other side bigger and better with plans to welcome even more visitors to the borough in the future.
"Along with the new Metro line, VLR, the bus interchange and plans for a university park, the future is looking very bright for the borough."
Glenis Williams, community engagement manager at the museum, said: “Forging Ahead is about so much more than just bricks and mortar: it’s about connecting people to the stories we’re discovering from the 1940s-60s.
"It’s about revealing hitherto hidden histories and representing the diversity of the Black Country.
"It’s also about finding creative ways to support the health and wellbeing of our community. For example, using the power of reminiscing about the 1940s-60s to amplify our work with Alzheimer’s and dementia groups.
"I’m excited about the impact Forging Ahead will have on helping us to deliver even more for our community."
Woodside Library, which opened at the end of the 19th century, has been closed since 2008. Last month a planning application was submitted by Dudley Council requesting permission to start deconstruction works.
Meanwhile the Elephant & Castle, which was pulled down in 2001 – prompting fury among residents – will be recreated using detailed archival research.
Investment for the expansion has also come from the National Lottery Heritage Fund and Black Country Local Enterprise Partnership.
It is hoped that the new historic town and industrial quarter will be open to welcome visitors in 2023, with the visitor centre opening next year.
It is expected to create more than 140 new jobs and contribute an extra £102.5m to the economy over the next decade.
The development will expand the museum’s footprint by about a third and increase its capacity to around 500,000 visitors per year by 2026.