The Devizes Assize Court Trust has appointed Purcell to the project.
Recent Purcell projects include Aerospace Bristol (home of the Bristol Aircraft Collection and Concorde), Kresen Kernow (The Story of Cornwall & Cornwall Archives) and St Fagans Museum of Welsh Life in Cardiff.
Purcell will be developing ideas for the restoration and adaptation of the historic Assize Court as well as planning a new extension fronting onto the Kennet and Avon Canal. The brief for the firm outlines requirements for exhibition galleries, café, shop and museum storage as well as community spaces, including meeting rooms and a large event and lecture space.
Additional work will be undertaken to identify how the building will be used for education including school groups, as a venue for local people for functions and perhaps weddings, and for tourists who can learn about the history of Wiltshire and the Assize Court.
The Devizes Assize Court Trust is planning to apply to the National Lottery Heritage Fund for significant support for the project during the next 12 months.
It is expected that the regeneration project may take ten years to complete and cost more than £10m.
Peter Troughton, chair of the Devizes Assize Court Trust, said "Appointing Purcell to be the architects of this exciting project is a significant step in rescuing the Assize Court building and moving the world famous Wiltshire Museum to its new home.
"There is much to be done to realize this vision, but with the help of the people of Devizes and many others, I am confident that we can achieve it."
Purcell partner Niall Phllips added: "Creating a new home for Wiltshire Museum at the Devizes Assize Court is a wonderful but challenging project that we will enjoy applying all our architectural and conservation skills to ensuring has an outstanding end result.
"Its success will reinvigorate the museum and its collections making them more accessible to wider audiences, it will resolve the future of a prominent but derelict historic building in the heart of the town and act as a flagship for its regeneration."
Support for the Assize Court Project has been received from: Wiltshire Historic Buildings Trust; Historic England; Architectural Heritage Fund; Pilgrim Trust; Dulverton Trust; Wiltshire Council – Devizes Area Board grant; anonymous donation and additional private donors; fundraising quiz organised by Catherine Drage; Calne Rotary Club; and sponsorship from Hunter French Estate Agents.