The practice fought off competition from Panter Hudspith, Tony Fretton Architects, Caruso St John, van Heyningen and Haward, and Jamie Fobert to pick up the commission.
These baths will be a permanent exhibit, forming part of the exhibition that will explore the history of Chichester and its district.
The project will also include a residential development on part of the site, which Williams will also design, in order to fund the scheme.
Keith Williams said: 'We are delighted to have come out ahead of a very strong field to win this prestigious project.
'We are looking forward to developing our concepts with Chichester District Council and its project manager RLF for a fine new museum in this historic city,' he added.
Development work has started on the £6.6 million project. It is hoped that the new building will be opened in 2010.