The axing of Apex means only two consortia are left in the race headed by Bouygues and Skanska.
The Bouygues Consortium comprises Bouygues UK Limited and Ecovert FM while Skanska includes Skanska Infrastructure Investment, Skanska Construction UK, Skanska Facilities Services and OCS.
The three groups were shortlisted last November beating off competition from Brookfield, Balfour Beatty and Sir Robert McAlpine.
Stephen Bridge, Chief Executive at Papworth Hospital, said: “This is a key milestone in the project to relocate Papworth Hospital NHS Foundation Trust onto the biomedical campus in Cambridge.
“We are looking forward to working with the two consortia to develop a new Papworth Hospital which provides the highest quality environment in which to provide the best care for our patients.”
Hospital chiefs will now work with both consortia on developing the design, build, finance and operate deal with a winner due to be announced in late 2012 and construction complete by 2015.