Ministers met earlier after delaying the decision, saying they wanted more information about risks.
There have been other modest changes to Covid-19 restrictions, including an increase in the number of people who can meet indoors.
Fully vaccinated people returning to the North of Ireland from so-called amber countries will not have to quarantine.
As part of the move to allow theatres and concert venues to reopen, the executive has agreed live music will be permitted for rehearsals and performances with no restriction to background ambient levels of volume.
Audience members must purchase tickets in advance, must have allocated seating and social distancing of 1m (3ft) will be required.
Meanwhile, 10 people from three households will be allowed to meet inside a home, with children aged 12 and under not counting towards that total.
Previously the rules permitted six people from two households to meet inside, with up to 10 people allowed if one household was bigger than six people.
The Executive also agreed that people attending religious services will not have to wear face coverings during the service.
It will be guidance only to wear a covering.
It will still be a legal requirement to wear face masks when entering and exiting the building.
Ministers will also strongly advise their use when singing or when moving around during services.
Earlier on Monday other rules changed, including allowing 15 people from unlimited households to meet outdoors and close-contact services being allowed to operate without the need for pre-booked appointments.
The executive will meet again on Thursday to consider other Covid-19 restrictions.
It comes as another 639 positive cases were reported by the Department of Health on Monday but no further deaths.Tags: