The contractor beat Sir Robert McAlpine to the prestigious job where construction will start later this month.
Willmott Dixon would not confirm the contract value but it is listed at £70m by construction information specialist Glenigan.
Work on the Somerset Road site next to the Wimbledon venue will see Willmott Dixon demolish the existing indoor courts and replace them with a new facility for AELTC members and competitors.
The project includes 12 new tennis courts (six indoor and six outdoor) and associated Club house facilities.
A single-storey underground car park for up to 338 vehicles will be the hub of The Championships’ courtesy car operation.
The building’s double-curved roof structure and surrounding landscaping will ensure it blends in sensitively with the local area.
Work is programmed to be completed by the end of October 2021.
Roger Forsdyke, managing director for Willmott Dixon in South London and the South East, said: “We are looking forward to be working with The All England Lawn Tennis Club to create these superb new facilities in a location that is synonymous with excellence in everything associated with tennis.
“We’ll be bringing our experience of working in live environments to ensure we keep any impact of work on the local community to an absolute minimum.”