The De Morgan Museum, based at Cannon Hall, forms the unusual offer of a museum-within-a-museum.
Awarded by Arts Council England on behalf of the UK Accreditation Partnership, it is the benchmark for well-run museums and galleries.
Director of the De Morgan Museum, Sarah Hardy, said: “Achieving accreditation for the first time is a huge milestone for the De Morgan Foundation, especially considering it’s a tiny, independent charity which receives no government funding and has only myself as a member of staff.
“This accolade has provided a solid foundation on which to build our future plans.
“Being awarded accreditation status demonstrates to the public that we are working hard to care for and promote this unique collection in perpetuity.
“I hope that everyone in Barnsley will be very proud to count De Morgan as their new local museum.”