Royal Engineers are helping to set up NHS Nightingale Hospital Exeter.
It is the latest in a series of NHS field facilities, which have been set up to ease pressure on the health service during the coronavirus pandemic.
Of the seven planned Nightingale hospitals in England, the site at Moor Lane in Sowton is the only one yet to become operational.
It is designed to provide regional support to Devon, Cornwall and neighbouring counties, supporting the existing network of hospitals there, the NHS has said.
As well as treating the sickest patients, it is understood the Exeter site could also be used by those with less severe coronavirus-related problems, as well as people recovering after a period in hospital.
The hospital's Medical Director, Rob Dyer told Forces News: "We can take patients who are very ill, who need mechanical ventilation and in fact the whole unit is set up to provide mechanical ventilation in 120 beds.
"We think it’s more likely that actually that we will have patients that are needing what you might call 'ward-level care' with chest problems.
"It will feel more like a hospital ward, I think, but with the ability to provide that more intensive care when we need it."
NHS leaders in Devon say that they hope that Nightingale Exeter will not be needed but, if or when it is, it will be ready.
Thirty-six thousand square feet of space is being converted to a hospital with 120 beds, with the work expected to be completed by late-June.
The hospital's Chief Executive, Philipa Slinger, said: “It’s an absolutely huge task. Lots of things to try and run sequentially that perhaps under normal circumstances you'd do in a more staggered phase.
"Lots of people on site, lots of lorries and deliveries, huge amount of planning, really complicated and big task."
To support this number of beds, 450 NHS clinical staff from across the region would work there.
Ms Slinger added her team has "really loved working with our military colleagues" and they are "very grateful to them".