BAM Construction won the tender via the government's Pro-Cure 22 healthcare framework.
The health trust announced last week that funds had now been secured through NHS Property Services to progress its redevelopment plans through to full business case and approval by its governing body.
Health sector specialist Medical Architecture will partner BAM to carry out a full detailed technical design to allow the scheme to go to planning. The two companies have worked together on previous healthcare schemes.
BAM construction director Paul Cleminson said: "Hospitals are complex buildings. The ProCure22 framework is an excellent way to tender major capital works because it allows early engagement for all the key partners to price it more completely and to identify and minimise the risks. It also means we form partnerships at the outset. That is a beneficial way to proceed when delivering something as much needed and important to local people as these new facilities are."