The Government has released its "green list" of destinations for safe travel, with Italy and Greece included but Britain a notable omission.
People arriving from Malta, Finland, Norway, Italy, Hungary, Estonia, Latvia, Lithuania, Cyprus, Slovakia, Greece, Greenland, Gibraltar, Monaco and San Marino will not be required to isolate for two weeks.
Others arriving from overseas - with limited exceptions such as essential supply chain workers - are required to fill in a passenger locator form and self-quarantine for 14 days.
People crossing the border from Northern Ireland are not subject to restrictions on their movement.
The list was published just before midnight on Tuesday after a late-night Cabinet meeting.
Britain and the US were expected to be excluded, as only places with a coronavirus infection rate the same or lower than Ireland were allowed on the list.
Holiday destinations such as France, Spain and Portugal have also been omitted.
The Government said it would "continue with plans to strengthen the existing measures for monitoring passengers who arrive into Ireland".
It said that included the introduction of an electronic passenger locator form, enhanced follow-up procedures and a proposed testing regime for symptomatic passengers at airports and ports.
It added that it would consider processes to restrict flights "in certain circumstances".
"The pandemic is not over and the public health advice remains the same. The safest thing to do is not to travel," the Government statement said.
The list was labelled as confusing by opposition parties prior to its release.
The Government has been accused of mixed messaging as it has published the list despite still recommending against non-essential travel to anywhere outside the island of Ireland.
Social Democrats co-leader Roisin Shortall said the "big weakness" in Ireland's pandemic response is the failure to control the importation of the virus from abroad.
She said: "The promised announcement of the green list for countries considered as safe while at the same time advising against all non-essential travel is inherently contradictory.
"But of much more concern is the Government's ambiguity about travel from countries that are not on the green list.
"Not only has the Government operated a self-isolate policy which has been largely unenforceable over recent months, but, inexplicably, in the last few weeks the travel advice has actually changed and weakened for those countries.
"Incoming travellers are now advised to merely restrict their movements.
"This poses a huge risk to our health, the lives of our vulnerable and to our economy."
Thirty-six new confirmed cases of coronavirus were announced in Ireland on Tuesday, taking the overall tally to 25,802.
No further deaths were announced on Tuesday, with the death toll remaining at 1,753.