The runway improvements will form the first phase of a £25m development plan, which also include building a new terminal building.
Bosses hope to invite contractors to tender for the runway construction project in late summer and expect work to begin before the end of the year.
The airport, also known as London Ashford Airport, is now nearing completion of several S106 conditions following planning permission for the runway extension last year.
Lydd Airport Executive Manager Hani Mutlaq said: “Capita has a wealth of experience in the highly specialised area of designing and building transport infrastructure, and was selected for this project partly on the basis of its recent work on the design of a similar runway extension at Southend Airport.”
Once completed, the extended runway will enable B737-type aircraft to fly with a full payload of passengers, maximising the availability of routes and aircraft choice to operators.