The building, in Glasgow's Merchant City, will also become home for the artist, who is best known for his contentious religious drawings and for painting Madonna in the nude.
A key feature of the £750,000 project is a glass-walled studio space, which will allow passers-by and visitors to watch Howson and his students at work.
Derelict for more than 30 years, the bathhouse's existing sandstone shell will be retained. However, RMJM intends to build a new rooftop to house the artist's apartment.
The Bath-House Gallery project is the first venture for The Third Step, a charity created by Howson to help recovering alcoholics and drug addicts as well as to promote access to the visual arts.
RMJM Director Paul Stallan said: 'We have worked closely with The Third Step, not only on developing the brief and lodging a planning application, but also giving advice on site acquisition, marketing, the business plan and exploring funding avenues.
'It is a fantastic project to be involved in and we are delighted to have the opportunity to work with Peter Howson and his team.'
The gallery is expected to open in mid-2006.