Earlier this year Dudley Council revealed the museum was to be closed down as a result of crippling financial cuts.
But last night, bosses unveiled a scheme to move exhibitions from the Dudley Museum and Art Gallery building in St James's Road to the Archives building in Tipton Road. This follows a petition signed by more than 4,000 people hoping to save the attraction.
Under the scheme the museum, which has geology and fine art collections, would neighbour Dudley Zoo and Castle, the Black Country Living Museum and the Archives in Castle Hill.
The old building will close as part of the move – as agreed in the budget earlier this year.
Tourism boss Councillor Khurshid Ahmed said: "It makes absolute sense to move the exhibitions to the Archives to benefit from the existing tourism at Castle Hill.
"We are carrying out some work at the Archives to make sure the museum is a popular attraction that welcomes people from far and wide to enjoy the exhibitions on geology and many more.
"We have met with campaigners and taken the time to show them around the Archives building and explain our vision to retain the exhibitions in a first class facility.
"These are really exciting proposals and will overcome all the issues we have had with parking and transport links at the current site, while creating something that will be as popular with school visits and people wanting to explore the steeped history of Dudley and everything that made this borough famous."
The borough's UKIP group leader Paul Brothwood said he welcomed the idea, but wanted the public seal of approval before backing the scheme.
Councillor Brothwood said: "I think the council has some severe lessons to learn and the community should have been involved from the start.
"Moving the museum to the Archives is a good move, but the big question is how we get visitors from the Black Country Museum, the zoo and the Archives to the town centre."
"Until that question is answered then we won't support this.
"UKIP will take this to the overview and scrutiny committee to make sure the community are onside and work out how we can best tackle this."
The council is holding talks with the owners of the museum's collections for permission to move them early next year.
It is hoped the new museum will open in summer 2017.
The old building in St James's Road will close at the end of this year while the council considers the future of the site.