Strict restrictions have been placed on visits to care homes during the last eight months because of the pandemic.
In new guidance, the Department of Health and Social Care says the "default position" is now that visits should be enabled to go ahead in all tiers – unless there is an outbreak in the care home.
Rapid ‘lateral flow’ tests, that can give people a Covid test result in about half an hour, are being rolled out to care homes in the county.
Health bosses say they are due to receive kits over the next four weeks.
The intention is that rapid regular testing will be offered to two visitors per resident.
Visits will be able to go ahead if they receive a negative Covid-19 test.
People are now being asked to be patient while measures are put in place to allow this to happen.
A statement from the Shropshire, Telford and Wrekin Sustainability Transformation Partnership (STP), said: “The national programme, led by the Department of Health and Social Care, to issue lateral flow testing kits to care homes is under way and our homes in Shropshire, Telford and Wrekin are due to receive kits over the next four weeks.
“The intention is that rapid regular testing will be offered to two visitors per resident, which, when combined with other infection control measures, appropriate personal protective equipment (PPE), social distancing and good hygiene will support meaningful visits.
“Whilst this is really welcome news, we need people to be patient with our homes as they receive their kits over the coming weeks.
"Care homes will have a lot to work through, including training their staff to support the testing, putting in place booking and logging processes and rolling it out for every one of their residents – this may take a little time.
"The local authorities and Shropshire Partners in Care will support homes and visitors with this programme."
The STP said that care homes were also keen to remind families and friends that the safety of their residents remains a priority and a negative test does not mean there is no longer a risk of transmitting the virus.
"People visiting their loved ones have a really important role in helping care homes to keep residents safe," it continued.
"Care homes will still be taking a measured approach to receiving visitors in a safe way, following robust infection prevention, and taking into account their specific circumstances and things like the layout of their home and the individual needs of their residents and staff."
When testing is finally under way, care homes will let families know by letter or email.
Visitors will also be reminded that they are still required to adhere to the 'hands, face, space' measures to keep their loved ones safe.