The scheme is set to start on Friday and run from up to seven venues across Wolverhampton - including the Civic Centre.
It will offer rapid turnaround lateral flow tests to people without Covid symptoms.
An initial 20,000 testing kits have been provided by the NHS, although council chiefs say they are currently unusable as crucial data recording devices have not yet arrived.
Similar schemes are set to be rolled out in other local Tier 3 areas, with Birmingham Council requesting logistical support from the Government to start city-wide testing.
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Mass testing is seen as a key element in boosting the region's chances of dropping down to Tier 2 when lockdown restrictions are reviewed on December 16.
Ian Brookfield, leader of Wolverhampton Council, said health chiefs in the city had spoken with NHS Improvement and were confident the missing kit would arrive ahead of the start of the programme.
"Providing the missing kit arrives we are ready to start mass testing next week," he said. "We are looking to use the ground floor of the Civic Centre as one of six or seven venues."
Mr Brookfield said the scheme would run on a similar model to the Liverpool pilot, which is credited with helping the city avoid Tier 3 restrictions after infection rates plummeted.
It will also feature a "targeted element", he added, with tests available for hospital workers and community nurses, as well as schools and the University of Wolverhampton.
The scheme is separate from the community-led pilot at the Sedgley Street Gurdwara, which is due to finish on Monday.
"This is a major plank in getting us out of Tier 3," Mr Brookfield said. "In Liverpool they halved their infection rate in no time, which shows the value in it.
"The more people we get tested the more we can curb transmissions, get out of the top tier and really help our hospitality industry."
Jane Stevenson, MP for Wolverhampton North East, said she wanted to see the city push for a similar level of mass testing as Liverpool.
"I want us to get to Tier 2 as quickly as possible and mass testing will help us get there," she added.
"Many people will carry and spread the virus without knowing they have it. Mass testing will identify asymptomatic cases and allow them to self-isolate."
Other parts of the region are planning to launch mass testing schemes.
Staffordshire County Council is hoping to start a programme over the next fortnight, which bosses say will eventually test up to 80,000 people each week.
Dudley Council also has a scheme in the pipeline.