They will open in Madeley at The Anstice tomorrow and in Newport at Cosy Hall on Wednesday.
Several pharmacies are also offering rapid tests across Telford and Wrekin with more set to open in the coming weeks.
People can book rapid tests online at each of these sites and results will be available in 20-30 minutes.
The rapid, lateral flow tests are available to residents who do not have any symptoms.
Those aged 11 years and over can book at a pharmacy and those over 16 can book at a council-run site.
More Covid-19 coverage:
Telford & Wrekin Council is encouraging those who can’t avoid leaving home for work to get a rapid test every three to five days.
These new sites are in addition to the existing rapid test site at The Place in Oakengates.
The rapid test involves you taking your own throat and nose swab and passing it to a testing operative, who will process the results.
The sites at pharmacies are part of a national scheme and is being delivered by a number of community pharmacies in the borough.
Liz Noakes, Telford and Wrekin’s director for public health, said: “One in three people who have coronavirus never show any symptoms but they still can be infectious.
“Testing people without symptoms will help us to identify and disrupt the chain of infection.
“It might seem odd to get a test when you feel well, but the earlier we can find positive cases the quicker we get people into isolation to prevent the spread of this virus.
“Those who can’t avoid leaving home for work should get a test every three to five days, especially if they are in contact with more vulnerable people.”
Andy Burford, cabinet member for health and social care, said: ”Making these lateral flow tests more available to residents is just one element in the fight against coronavirus, we must continue to do the essential – staying home, wearing a face covering, washing hands, and keeping two metres distance.
“Even if you test negative one day, you can still contract the virus at a later date.
"If you show signs of any of the main symptoms, you must get a full Covid test at one of our four test centres.”
To find out which pharmacies are taking part, or to book a test at a pharmacy, search rapid test Telford or visit rapidtest.telford.gov.uk