The delayed landmark building was due to open last year but AstraZeneca said that while staff will start occupying parts of the building this year practical completion is not expected until the end of 2021.
Skanska signed a £330m contract five years ago for the construction management of a research and development centre and corporate headquarters.
Mace replaced Skanska on the major project two years ago after big costs overruns and delays were first revealed.
At the time the project was running a year late and expected to cost £500m.
The latest review by Mace as the project nears completion now puts the final cost at around £1bn.
In its annual financial report, AstraZeneca said that activities were well advanced after a focus last year on fit-out of laboratory and scientific support spaces, and interior design of the office areas as well as landscaping.
The report stated: “Following the review of costs by the new construction manager, the latest cost projection for the R&D centre is in the region of £1bn.
“Costs for the project have risen since our original projection due to the complexity of the build, construction cost inflation, including the impact of a weakening pound, and increased investment in new technologies and equipment as part of our ongoing investment in R&D in the UK.”