Health Minister Eluned Morgan announced the changes on Wednesday, bringing the country in line with the rest of the UK.
Since Christmas Day, daily bookings at test sites across Wales have reached up to 28,000 – a record high.
Baroness Morgan said the change would be brought in from Thursday January 6 and is predicted to reduce the demand for PCR tests by between 5%-15%, helping increase access for those who have symptoms and need to book a test.
The minister said: “Together with the other UK nations, we have agreed that if a person showing no symptoms has a positive lateral flow test they will no longer be advised to have a follow-up PCR test to confirm the result, unless they are in a clinically vulnerable group which may need early access to treatment or have been advised to do so as part of a research or surveillance programme.”
She said data suggests that lateral flow tests and PCRs have a similar positive predictive value when the prevalence of coronavirus is above 1%, as it is currently.
Unvaccinated contacts of positive cases who are self-isolating for 10 days will now be asked to take a lateral flow test on day two and eight instead of a PCR test.
This change will come into effect immediately, the minister said.
She added: “We may need to introduce further changes to protect PCR tests for key workers through the UK testing programme if demand continues to grow in the coming days and weeks.
“We need everyone to continue to play their part in disrupting the transmission of Covid-19 by reporting their lateral flow test results on the gov.uk website or by calling 119.
“We recognise these changes will potentially increase demand for lateral flow tests. There are no current issues with supplies but we are aware of issues with distribution for people to access tests at some collection points including pharmacies.
“UKHSA manage the logistics and deliveries across the UK and we are working closely with them to improve the situation. More than four million tests were distributed to workplaces, people’s homes and collection points in Wales last week.”