The unit will be the second to be operated by the national NHS Test and Trace service in the Telford and Wrekin borough and is aimed to boost capacity in the area.
It was being set up in the Randlay Valley Car Park.
There have previously been long queues for tests in the borough, with chaotic scenes at Jiggers Bank in Ironbridge earlier this month as people were denied access despite waiting in heavy traffic.
One father drove his two ill children for more than two hours to Ironbridge only to be told the centre had "run out of tests".
Similar scenes have happened across the country with some people in the West Midlands told to go to Aberdeen when requesting a test online.
Telford and Wrekin currently has one of the lowest infection rates in the West Midlands, with 20.8 cases per 100,000 people in the seven days to September 21.
The rate in the Shropshire Council area is similar at 20.3 per 100,000 people, with both boroughs substantially lower than in Wolverhampton (66.4), Sandwell (94.7) and Birmingham (122.2) where local restrictions have been introduced banning households from mixing.
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Telford and Wrekin's cabinet member for health and social care Councillor Andy Burford said: “We’re really pleased to welcome this drive-in mobile testing unit to Telford and Wrekin.
“It is so important to be able to offer testing for the virus as close to people’s homes as possible.
“Tests are available by appointment only to anyone with symptoms – so that means a new, continuous cough, a high temperature or a loss or change in their sense of taste or smell.”
Hollinswood & Randlay Parish Council clerk Katrina Baker said: “We are pleased to have been able to support this important facility and to work with Telford and Wrekin Council and NHS to enable the drive-in mobile testing unit to be here in Randlay.
“It is a site which is close to the town centre, Stafford Park and Hollinswood and we hope that it will assist in supporting the initiatives and guidelines that are in place to help keep people safe locally”
The council plans to open several new walk-in testing centres for those without a car within the next few weeks.
Anyone with coronavirus symptoms, however mild, can get a free swab test with tests available to book at nhs.uk/coronavirus or by calling 119.