The £1.9bn turnover caterer, which also owns more than 100 stores in education campuses and 14 in Ministry of Defence bases, said its retail arm could potentially grow as large as its catering business.
Four of the McColl's stores have been rebranded to Compass's Amigo fascia, with the rest to be converted by September.
Ian Sarson, Compass's MD of specialist markets, said consumers increasingly wanted food-on-the-go rather than sit-down meals.
"We see food-on-the-go as becoming an increasing part of people's daily life at work, even in a recession, and our c-store format addresses that," he said. "It's part of the business that is in good growth and is becoming a part of our core business."
The stores are expected to turn over £35m a year, with £25m coming from sales of food-to-go, such as hot pies, coffee, fresh fruit and snacks.
"We can bring our traditional strengths to our Amigo service," Sarson added. "Stores in hospitals don't sell tobacco or alcohol, which are two of the most important categories for many c-stores, and we plan to make use of our expertise in food-to-go to make sure our offers are as convenient as possible."
He added hospital staff that "are time-poor and want food-on-the-go" would use the stores as much as visitors.