Anyone without symptoms of coronavirus is invited to get a free test by visiting the unit, which is situated outside the Urgent and Emergency Care Centre, between 11am and 8pm every day.
People are asked to arrive for their test at least 30 minutes before their visiting time to ensure they can receive their result.
Professor David Loughton CBE, Chief Executive on The Royal Wolverhampton NHS Trust, said: “We are pleased to be taking this step forward in the reintroduction of visiting to our hospitals. Suspending visiting has been very difficult for our patients and staff so I am really glad we can start to ease our restrictions.
“Protecting patients and staff is our top priority and we have put in a number of safety precautions to make sure we reinstate visiting in a safe and compassionate way.
“One of these measures is we are strongly encouraging all visitors to take a rapid Covid-19 test beforehand. Wolverhampton's mobile test unit is now at the hospital for visitors to use at their convenience. Please allow an extra 30 minutes before your visiting slot to get tested and for your result to be made available.
“We would like to say thank you for your continued understanding and patience during this difficult time.”
John Denley, Wolverhampton's Director of Public Health, said: "1 in 3 people with Covid-19 do not have any symptoms but could still spread the virus to family and friends.
“Rapid testing is helping to identify these asymptomatic cases and reduce the spread of infection, and we're pleased to be working with The Royal Wolverhampton NHS Trust to offer rapid testing to protect patients and staff and safely enable hospital visiting once again.”
People can also get a free rapid test at the Civic Centre, The Hub at Ashmore Park and the Jamia Masjid Bilal, while free home test kits can be collected from the mobile unit, the Civic Centre, The Hub at Ashmore Park, PCR test centres, Bilston Market, Wolverhampton Market, WV Active Aldersley, WV Active Bilston-Bert Williams, WV Active Central, Wolverhampton Swimming and Fitness Centre and local pharmacies offering the Pharmacy Collect service (details at NHS - Find where to get rapid lateral flow tests).
Up to 2 boxes can be collected at a time, containing a total of 14 home test kits. The kits include step by step instructions to complete the test, and people are reminded they should register their result, even if it is negative.
More information on rapid testing, including advice about how to take the test at home, is available at Lateral Flow Home Test Kits.
Please note, rapid testing is not available for people with coronavirus symptoms. Anyone with symptoms, including high temperature, a new or continuous cough, or a loss or taste or smell, should book a PCR test at NHS - Coronavirus (COVID-19) or by calling 119.
