The client is Chichester District Council and the project is expected to be completed by spring 2014.
The new brick and steel building will be a combined leisure and health centre, community hall, library and café.
The building has been designed to be flexible, offering a range of different activity areas. Some rooms have moveable walls, allowing the centre to expand areas, or reduce them, depending on the activity.
The new centre is to replace the town's Grange Centre, which is in disrepair and is not fully accessible to people with disabilities.