A small number of restrictions are currently in place, including the wearing of face coverings and the use of Covid certification in nightclubs.
Mr Swann said those remaining measures “should no longer be set out in regulations” and instead will be put in guidance issued to the public.
He said he would be making an order on Tuesday to revoke the remaining rules.
Remaining restrictions include requirements to wear face coverings in public places; for business owners to have measures in place to limit transmission of the virus; for the use of Covid certification at nightclubs and large unseated indoor events; and for limits on numbers meeting indoors in private homes.
“This does not mean that Covid-19 has gone away or that we as a community are safe from its harm,” Mr Swann said.
“It is vitally important that we continue to observe the sensible measures we have all learnt to protect ourselves and others.”
The health minister said it was important to retain the ability to reintroduce restrictions again in case of urgent need.
As a result he said he will seek to extend the powers granted to the Department of Health by the Coronavirus Act 2020 by six months.
Mr Swann had written to his ministerial colleagues asking for their views on removing remaining restrictions.
The executive collapsed earlier in February but individual ministers are still in place.
They can take some decisions, as long as the issues are not deemed “significant or controversial”.
Mr Swann’s letter to other ministers said government lawyers had told him relaxing Covid rules would fall into this category.
He said the lawyers suggested he could therefore not remove the rules by himself, under the terms of Stormont’s ministerial code.
On Monday, two more Covid-related deaths were announced in Northern Ireland along with 2,465 cases.
There are currently 437 patients with the virus in hospital.
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