The moves were dependent on the R-number staying below one when ministers met on Thursday morning.
From Monday, vulnerable people advised to shield will be allowed outdoors.
Large retailers including car showrooms and shops in retail parks can also reopen, and outdoor weddings with 10 people present will be allowed.
But there is still no news on when hairdressers, barbers, restaurants and bars can reopen to the public
The R-number, or reproduction number, is the average number of people that one coronavirus-infected person will pass the virus on to.
Last week, the executive said the R-number in Northern Ireland was sitting at 0.9, and that it would only allow more restrictions to be eased if it was still below one when it met on Thursday.
Ministers received an update from the executive’s chief medical officer and chief scientific officer about where the R-number was sitting, before they could confirm the changes that had already been provisionally announced.
It is understood the executive is not expected to announce plans to lift any other restrictions at this stage.
The executive’s five-step Pathway to Recovery does not include a timetable for each of the phases, but agreement on allowing these moves to begin means Northern Ireland will have implemented some of step two in the blueprint.
Measures that the executive will allow from 8 June include:
Small weddings and civil partnership ceremonies permitted outdoors, with no more than 10 people present;
Outdoor sports courts, horse trainers and dog groomers can reopen;Hotels will be able to take advance bookings, ahead of a planned reopening on July 20;
Large non-food retailers can reopen, including car showrooms, electrical shops and phone shops;
About 80,000 people advised to shield can go outdoors with their household; or if they live alone they can meet one person from another household.
Ministers have stressed that people and businesses must still adhere to physical distancing rules, by staying 2m (6ft) apart.
The North’s recovery from lockdown will not be “calendar led”, and it is likely aspects of different steps of the Pathway to Recovery could take effect at the same time, the executive has said.
On Monday, First Minister Arlene Foster criticised reports of complacency and a “flagrant disregard” for the lockdown restrictions.
“You prolong the journey out of lockdown if you break rules and create conditions where Covid-19 can thrive,” she warned.
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