The size of extended households can be increased to up to three households, and a further household with a single adult or single adult with caring responsibilities will also be able to join.
The move to alert level one will be phased, with outdoor events opening first. Ministers will review the public health situation again, ahead of June 21, to determine whether indoor events can restart.
The two-stage approach is intended to enable more people to be vaccinated – and complete their two-dose course – amid growing concerns about the spread of the delta variant of the virus across the UK.
The seven-day coronavirus case rate remains very low in Wales and the positivity rate is less than 1%. Wales also has the best vaccination rates in the UK – more than 85% of the population has had one dose and 45% have completed the course.
But there is growing concern about the spread of the delta variant in many parts of the UK, especially in the North West of England.
There are currently 97 cases in Wales, including a cluster of cases in Conwy.
The first phase of the move to alert level one means that from Monday June 7:
The Welsh Government will consider further changes to the regulations on indoor activity later in the month, if public health conditions allow.