The pub on Hare Lane, located close to Sandown Racecourse, will include a 55-cover restaurant area and 14-cover private dining room.
The style of the menu, overseen by Claude with head chef Justin West, is described as 'English food from a Frenchman' with dishes to include Lyonnaise salad with poached eggs, organic bacon and crispy croutons, rump of Welsh spring lamb with Moroccan mint pesto; The Swan burger and desserts such as treacle tart with clotted cream and Rhubarb jelly and custard with Scottish shortbread.
Lunch will be served from noon to 2.30pm and dinner from 6pm to 9.30pm Monday to Friday with food available from noon to 9.30pm on Saturdays and until 8.30pm on Sundays when a roast will be available all day.
West, who has worked with Claude at his two Michelin-starred restaurant Hibiscus, will work alongside manager Joseph Hendriks, who has also worked at Hibiscus and at Claude and Cedric's pub The Fox & Grapes in Wimbledon, which they helped launch in 2011.
Claude remains chef-patron of Hibiscus while Cedric continues to own The Charlton Arms in Ludlow, Shropshire and the Townhouse Hotel, also in Ludlow.
The brothers were previously involved with The Fox and Grapes in Wimbledon and The Malt House in Fulham.
The Swan Inn is recruiting for front-of-house and kitchen staff. For more information and to apply, visit jobs.bighospitality.co.uk.