The centre, known as OMA, will integrate the town’s existing Victorian Grade 2-listed former library and its current arts centre.
Contractor Gilbert Ash was previously engaged by the council on the project under a pre-contract services agreement.
But the council has now selected Interserve using the Procure North West framework.
OMA will showcase the story of Oldham’s past from its time as the cotton spinning capital of the world to the present day, with gallery spaces, archives and public research rooms.
Councillor Sean Fielding, Leader of the Council and Cabinet Member for Economy and Enterprise, said: “This is another great step in the regeneration of our town centre and our plans to make Oldham a cultural destination.
“Interserve has a strong track record in delivering similar projects to a high standard and were responsible for restoring the Corn Exchange in Manchester.”
Phil Shaw, divisional director at Interserve Construction, said: “Our team has significant experience of working on historic buildings like Oldham’s Victorian library and we will be bringing our expertise and capabilities to the project by adding a contemporary and modern addition to the building while respecting its architectural heritage.”