The translucent roof, which was revealed by Building last May and is aimed at ensuring rain no longer stops play, is to be built by 2009.
A source close to the project said: "Construction work on the roof could cost £50m. It's not just a case of remodelling the roof and then sticking on a cover to keep the water out. You have also got to upgrade the M&E side to take account of the humidity."
Estimates in newspapers this week suggested the project could cost £100m, but this would include additional stadium changes and safety provisions when work shuts down for the championships.
Architect HOK Sport's scheme uses a folding fabric concertina design, which is similar to an umbrella, to allow the roof to be folded into a compressed area when it is not in use.
When fully extended, the fabric would cover an area of 65 × 70 m, only slightly less than the roof of Cardiff's Millennium Stadium.
HOK Sport principal Rod Sheard described the roof scheme as the most difficult project the company had ever worked on.
He said: "It was a very technically demanding challenge. We've been working on the project for three years, two in secret, gathering information from the court. We didn't want to manipulate the traditions of Centre Court."
HOK Sport's design enables natural light to reach the grass and keeps the temperature inside at a constant 24°C with 50% humidity.
The roof, which is designed to be put into position in 10 minutes, is understood to be the first of a series of HOK Sport stadium projects incorporating the concertina-style folding structure.
As well as the roof, HOK Sport will strip the world's most famous tennis court down to its original 1922 design. Six rows will be added to the upper tier on three sides, increasing capacity from 13,800 to 15,000 spectators.
The ticket office and retail areas in the east stand are being moved to the east of Centre Court in a separate development scheduled to finish by early 2006. Completion of the Centre Court work is planned for 2009.