Visitors will be allowed to enter the country as long as they test negative for the virus upon arrival.
Iceland, which has a population of around 364,000, has had 10 deaths and just 1,802 confirmed cases, according to the online dashboard from John Hopkins University.
The government announced the plans earlier this week, with Prime Minister Katrin Jakobsdottirsaying in an official statement that travel restrictions would be loosened 'no later than June 15 2020', while 'from May 15 some professionals arriving in Iceland including scientists, filmmakers, and athletes will be eligible for a modified quarantine'.
Thordis KolbrunReykfjordGylfadottir, Minister for Tourism, added: "When travellers return to Iceland we want to have all mechanisms in place to safeguard them and the progress made in controlling the pandemic.
"Iceland's strategy of large-scale testing, tracing and isolating have proven effective so far.
"We want to build on that experience of creating a safe place for those who want a change of scenery after what has been a tough spring for all of us."
The Icelandic government has said travellers to the country will likely be required to download and use the official app, which has been developed with privacy measures - with location data only stored locally on the user's device, unless it has to be released for tracing purposes after an infection is confirmed.
Icelandair is reportedly struggling as flights drop to an all-time low, with 3,000 members of staff being laid off.
Responding to the news, Bjarnheiour Hallsdottir, the Chair of the Icelandic Travel Industry Association, told RUV News: "It's very important to be able to have a more long-term view of things than we've been able to until now.
"I believe that if everything goes well, we should see some tourists here this summer. For those who want to come, this will be a very real possibility.
"There is a lot at stake that Icelandair continues operations, and it's in reality a life-or-death question for tourism in Iceland.
"Hopefully people realise that the situation isn't just about Icelandair but tourism in Iceland as a whole, and not just tourism but the economy and our whole society."
Chosen for YouChosen for You
Most Read StoriesMost Read