The facility is based at the Wrekin Road Car Park in Wellington and is the latest in several new walk-through testing centres set to be opened in the coming weeks.
The idea is to make testing more accessible for those without a car.
More Covid-19 coverage:
Anyone with one of the three key coronavirus symptoms, however mild, can get a free swab test at the site that takes less than a minute.
Tests at the site should be booked or ordered as soon as symptoms begin at nhs.uk/coronavirus or by calling 119.
Andy Burford, Telford & Wrekin Council's Cabinet Member for Health and Social Care, said: “Making testing accessible to all is important, not everyone has a car and we need to be testing everyone in Telford and Wrekin who has symptoms to prevent the spread of the virus.
“The council has worked hard with Government to open these centres by providing them with a number of suitable sites to choose from.
“Each site was assessed for accessibility and security; also additional signage is being installed by the council to prepare the site.”
The council said information about locations and dates of future walk-through centres will be released when details are finalised.