The centre, which houses artefacts for the whole county, including internationally important geology samples, was awarded the money as part of Chancellor George Osborne's Budget.
The news is a much-needed boost for the Shropshire Council-run centre, which saw its staffing cut from three experts to one part-time curator post earlier this year, despite an outcry from more than 1,000 supporters.
The centre was one of a handful granted money from the Libor fund – a pot of money from fines imposed on banks for breaching regulations in 2012 – in the Chancellor's Budget for 2015.
Ludlow MP Philip Dunne said he had contacted Mr Osborne in the spring to set up a meeting between Treasury Officials and the Friends of Ludlow Museum, who made a case for the national significance of the collections housed in Ludlow.
John Cherry, a former curator at the British Museum and a member of the Friends of Ludlow Museum, Lottie James, chairman of the Friends, and Mr Dunne all spoke on behalf of the museum and resource centre.
Mr Dunne said today: "This funding is a real boost for Ludlow, for all those in Shropshire who use the museum, and for the wider scientific community.
"The Museum and Resource Centre has been well used for many years by local schools, interested volunteers and eminent scientists. I am delighted that this funding will help ensure continued use and improved access for the future.
"In recent months Friends of Ludlow Museum developed credible plans to create a digital record of the county collections maintained in Ludlow, which will facilitate lasting access to this national quality collection.
"I believe it is also the first time that the town of Ludlow has been specifically referenced in the Budget Red Book."
Andy Boddington, Shropshire councillor for Ludlow North and a supporter of the museum, added: "It must have been a good pitch because the grant to Ludlow Museum was one of just eleven Libor awards announced in Wednesday's budget.
"This is a brilliant result. This grant doesn't replace the need for Shropshire Council to properly fund its museum service but it does give national recognition of the importance of the geological collections in Ludlow.
"It also demonstrates what can be achieved if those dedicated to our museums, heritage and cultural sector engage in a bit of inspired thinking," he said.
Ludlow Museum and Resource Centre houses Shropshire museum collections not currently on display in the other local museums across Shropshire.
These include a natural history collection, archaeological collections, and the significant geological collection which comprises over 41,000 fossils and mineralogical specimens.