Live updates: follow the latest news on Omicron
From Saturday morning, restaurants and bars will be able to operate at normal hours, while Covid passes and social distancing will not be required.
Crowd limits will be removed for indoor and outdoor events, as will rules on the number of households that can mix. People can also gradually return to workplaces from next week.
The measures were introduced last month amid the spread of Omicron, a highly infectious variant of coronavirus.
“I have stood here on many dark days but today is a good day,” Mr Martin said in a televised address.
“We've concluded that the rationale or justification for continuing most of our public health restrictions are no longer in place.
“The majority of public health measures that we've had to live with will be removed,” he said, but added that “the pandemic isn't over".
Masks will still be required in certain instances. Self-isolation rules will also stay in place for those who test positive for the virus and their close contacts as well as symptomatic people.
Ireland, which has recorded more than 6,000 Covid-19 deaths, has had a high number of people receve vaccinated, with about two thirds of those over the age of 5 taking a booster shot in recent months.
“Ireland's first-class vaccination programme and the roll-out of boosters has utterly transformed our situation,” Mr Martin said in his address.
“It was our vaccinations and boosters that prevented the recent wave of infection translating into much more serious levels of illness and death.”