The firm beat shortlisted rival Bouygues after two years of final stage bidding for the £165m PFI hospital scheme.
The project will consist of a 310-bed, purpose-built hospital boasting single rooms and a research and education institute. But it still needs approval to proceed from the Department of Health and the Treasury before financial close of the PFI deal.
If all goes to plan, construction is set to start in Autumn 2014 and be completed by early 2017.
Project Director Ken Brewer said: “While the two bids were both very comprehensive the assessment of the bids followed a very robust process which resulted in the selection of the consortium led by Skanska.”
Chief Executive Stephen Bridge said: “This is an important milestone in the ten-year project to move to our new site on the Cambridge Biomedical Campus.
“In early October we heard that the Department of Health had cleared the business case to be forwarded to the Treasury for approval and today’s announcement will move us closer to realising our vision to provide the highest quality facilities for our patients”.
“The clinical, research and economic case for the new Papworth Hospital is beyond doubt and we look forward to relocating to the Cambridge Biomedical Campus which is fast becoming one of the most vibrant biomedical communities in the world.”