From Monday two households in Wales will be able to meet each other for the first time since the lockdown began, the First Minister is expected to announce later.
The meetings must take place outdoors and maintain the two metre social distancing rule.
People will also be asked to stay local and, as a general rule, not to travel more than 5 miles from their home.
Unlike England and Scotland the Welsh Government will not restrict the number of people who are able to meet.
In a video message posted on Thursday, Mark Drakeford thanked the people of Wales "for your ongoing help and support and for all the sacrifices you have made."
He added: "I know being separated from family and friends is difficult.
"During this review, we have been looking at how we can do this once more, in a very careful and cautious way, without increasing the risk of the virus spreading."
But the five mile rule has been labelled as "unfair" by one prominent Welsh Conservative.
Andrew RT Davies, the former Tory Senedd leader has written to the First Minister saying it would impact on rural Wales.
Mark Drakeford is expected to say "staying local will help keep Wales safe" at a press conference on Friday afternoon where the changes will be formally announced.
Exceptions will include travelling to work and shopping for essentials if they aren’t available locally.
Speaking on Good Morning Britain, Mr Drakeford acknowledged the five mile rule was "unfair" but said it was important to stop the virus being taken to the parts of Wales with the lowest rates of infection.
He also confirmed people will be able to meet in gardens but that the safest things was still to "see as few people as you can."
He said: "People should still be sensible about it. Do it only when it's necessary, stay apart from one another. Running through people's houses, sitting in gardens close together, having a beer and it all breaking down - that is definitely not what we are proposing in Wales."