Snap40 uses a predictive analytics software platform to identify, in real-time, those whose health is at risk of deteriorating.
The technology includes a single medical wearable device, worn on the upper arm, to monitor health indicators continuously.
Snap40 said the contract would help it further scale its technology.
It will also help fund ongoing clinical studies with NHS Fife and NHS Lothian's Emergency Medicine Research Group Edinburgh (Emerge).
Co-founder and chief executive Christopher McCann said: "In an ideal world, we'd all have our own dedicated doctor sitting with us, 24 hours a day, seven days a week.
"But, with increasing pressure on healthcare systems and challenges in prioritising competing demands, access to doctors and nurses is at a premium.
"Our society simply cannot afford one-to-one care - Snap40 changes that.
"It allows our world-class healthcare staff to care for many more patients by helping them to prioritise who needs attention most."
NHS Fife, which worked with Snap40 on the company's first clinical evaluation last year, is continuing to collaborate with the company
An Edinburgh tech firm has won a £1m healthcare development contract from NHS England.