The 44,000 sq ft (4,090 sq m) extension will comprise a 22,000 sq ft (2,045 sq m) retail unit and another 22,000 sq ft (2,045 sq m) unit designed for leisure use.
Existing tenants at the shopping centre include Tesco, Iceland, Boots, Peacocks and Lidl.
Edinburgh House managing director Tony Quayle said: 'Langney is currently underserved in terms of larger space leisure and retail facilities. The extension has been designed to provide modern accommodation that will fit with the requirements of the retailers we wish to attract.'
Hammond Phillips is letting agent.