Wales will remain in lockdown for another three weeks to avoid "a return of the virus" – but restrictions will be eased slightly from Monday.
He added that he believes that the R number (the rate of infection) of COVID-19 in Wales, was at 0.8.
That means an infected person will, on average, infect less than one other.
But he said that three changes will be made to restrictions from Monday.
- People will be allowed to go outside to exercise more than once a day – but that exercise must begin and end at home and must not include travel
- Garden centres can open as long as they adhere to social distancing guidelines
- Local authorities will begin planning how to safely re-open libraries and tips
Mr Drakeford went on to say that vulnerable people must continue to shield and over-70s should continue to take extra care, adding that he is committed to "keeping our people safe".
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He said that he expects 800 more people to join the "very sad and sombre list" of deaths – but that if lockdown was fully lifted, the number of deaths could reach 7,200.
The first minister told reporters that he believes any changes being made to the UK wide-restrictions, due to be announced on Sunday by Prime Minister Boris Johnson, will be modest, and broadly similar to those made in Wales.
However, he believes the small changes he has announced, will make a difference to people, without raising the R rate.
Mr Drakeford becomes the second UK leader to seemingly announce the government's intentions before Mr Johnson, but told Sky News that talking with Westminster has been working "well", and that they "are open and are engaged", but admitted he would prefer a more regular pattern of communication.