East Kent Hospitals tested 9,000 members of staff over five days last week and the results were announced on Tuesday.
The 15 staff who tested positive are now self-isolating at home in line with national guidance, the trust said.
The trust’s chief medical officer Dr Rebecca Martin said: “We know that while many people experience mild – or even no – symptoms of Covid-19, they have the potential to carry and pass on the virus without knowing it.
“Testing staff means we can be sure no member of staff who may be carrying the virus without knowing it is working in our hospitals.”
Kent has been under the spotlight after the region recorded some of the highest coronavirus death rates in the country last month.
Ashford, one of the county’s largest towns, saw the single highest mortality rate involving Covid-19 anywhere in England for June – with a rate of 36.5 deaths per 100,000 people, according to the Official for National Statistics (ONS).
The monthly mortality rate for Ashford has remained relatively consistent since ONS began gathering figures after lockdown, dropping only slightly from 40.7 deaths per 100,000 people in April to 36.7 in May and 36.5 last month.
East Kent runs three acute hospitals and serves a local population of around 759,000 people.
Dr Martin added: “It is important that our patients and staff have confidence that we are doing all we can to keep them, and those close to them, safe while they are in our care whether they are being treated for Covid-19 or using other hospital services.
“Patients can help minimise transmission of Covid-19 by following the advice to wear a face covering, regularly clean their hands, maintain social distancing where they can and following the instructions in the hospitals.”
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Earlier this week, The Independent revealed that both hospital patients and staff will be able to find out if they have Covid-19 within one hour under a nationwide testing programme being developed by the government.
A small, handheld device that can process samples on-site will be used to detect the virus from a non-invasive nostril swab.
The government has ordered up to 20,000 of the “lab-free” devices, set to be introduced in hospitals and health clinics across England between October and March.