The 108 bed block will be delivered to site next month and installed during a 16 week programme.
The building will have a 60 year structural design life with a 25 year structural warranty.
Dr Peter Reading, interim chief executive at Peterborough and Stamford Hospitals NHS Foundation Trust, said: “This build project will enable us to offer our staff good quality accommodation at the City Hospital site.
“The building has been created in a modular design which means it will be more straightforward to extend it in the future, if necessary.
“I am pleased that the Trust is able to work with a local company to develop the site and we look forward to watching it quickly take shape.”
Bernard Quenot, Managing Director of Elliott, said: “We have a long track record of providing high quality building solutions on time and within budget.
“Our off-site systems offer assured levels of quality as well as meeting all current regulatory requirements.”