The Cabinet has approved the move to Phase 3 of the roadmap to reopen the country, Taoiseach Leo Varadkar has said.
Speaking at Dublin Castle, Mr Varadkar said that following advice from the National Public Health Emergency Team and Government departments almost all remaining businesses and amenities can reopen from Monday 29 June.
He said some travel restrictions between Ireland and other countries will be eased from 9 July.
A "green list" of countries will be published prior to 9 July, with the 14-day quarantine that is currently in place not applicable to travel from these countries from that date.
The Taoiseach said this list of countries will be reviewed every two weeks and some countries could be added or removed depending on their infection rates.
Minister for Health Simon Harris said that the wearing of face coverings on public transport will be made mandatory. He said there will be a sanction for non-compliance.
Mr Harris said the move is necessary in order to allow capacity on public transport to increase.
He said there is clear public health advice that people should also wear face coverings in shops and other situations where they cannot practice social distancing measures.
Cabinet also agreed that there would be an exception to the regulations for churches to allow more people to attend religious ceremonies.
A grant scheme to assist people who are self-employed or sole traders has also been approved by the Cabinet to help people to get back to work.
The School Meals Programme is being extended for summer 2020 to all schools and organisations currently in the programme for the next nine weeks.
Mr Varadkar offered his condolences to those who lost loved ones during the pandemic, saying he hopes to have a National Day of Commemoration in the coming months.
He said we must "now try to repair the damage that has been done, across all parts of our lives, and show the same solidarity in doing so".
Mr Varadkar said: "It is possible that this is my last press conference as your Taoiseach, and if so, I want to end by saying thank you to the men and women who kept our country protected and guided us through this emergency."
He also said he believes the country "owes a profound debt to the Chief Medical Officer, Dr Tony Holohan, who has become one of the most trusted figures in the country and made us all feel that we were in safe hands."
From Monday, bars that serve food can reopen with table service only, while hotels, hostels, caravan parks, galleries and museums can welcome visitors again.