People who are fully vaccinated will receive their EU Digital Covid Certificates by either email or post from next Monday, under plans being finalised by the Government.
It is expected that a national call centre will be established to assist with any inquiries.
The cert is due to facilitate the return of non-essential international travel from 19 July, but could be expanded to include the recommencement of indoor hospitality.
Minister for Transport Eamon Ryan said that, from next Monday, the certificates will be sent out to the estimated 1.9 million people who are fully vaccinated.
It is understood that if a person was vaccinated after registering via the Health Service Executive portal, they will receive their documentation through email.
However, if a person received their vaccine through a GP, or a pharmacy, they will receive a letter in the post.
If a person contracts Covid and recovers, they can contact the soon-to-be established call centre, which will be able to issue them their EU Digital Covid Certificate.
No date for opening of the call centre has been set just yet, but government sources expect it will be functioning before 19 July.
Each letter will contain a code that can be scanned onto a smartphone.
The Tánaiste said he expects there will be "teething problems" with the implementation of the certificates.
Speaking on RTÉ's News at One, Leo Varadkar said: "I am sure there will be some people who don't get their certificates on time, so we'll have a call centre in place to help people out if that happens."
He said some initial delays in airports were possible and urged travellers to give themselves plenty of time.
We need your consent to load this rte-player contentWe use rte-player to manage extra content that can set cookies on your device and collect data about your activity. Please review their details and accept them to load the content.Manage Preferences
Mr Varadkar said passengers had to remember there were two sets of rules to adhere to - at their destination and on their return to Ireland.
"A lot of people think they need a PCR test to leave the country, they probably don't, but you may need one to return."
He said the certs will enable people who are fully vaccinated - or immune because they had Covid in the last nine months - to return from abroad without having to restrict their movements or quarantine.
People who have recovered from Covid will need a laboratory confirmation of this, alongside a negative PCR test.
Mr Varadkar said the public health advice on this is very strong - those who are not fully vaccinated or have not recovered from Covid should avoid international travel [before 19 July].
The minister said he expects to bring proposals to Cabinet next Tuesday on whether or not the digital certificates can be used as a basis to facilitate indoor hospitality.
A number of options are being considered, but it was not certain that the Government will be ready to implement those proposals by 19 July.
Mr Varadkar said "that would be ideal, but I can't say that for certain".
He said the use of testing is also under consideration as a criteria for availing of indoor hospitality but "there are difficulties" with it.
"We wouldn't have the capacity to carry out tens of thousands or hundreds of thousands of PCR tests for people to go to a restaurant or a pub."
It is understood that the issue of how the EU Digital Cert will apply to vaccinated people from Northern Ireland is still being worked on.
Earlier, Minister for Transport Eamon Ryan said he expects plans to resume international travel from 19 July to be "on track".
In relation to the further reopening of the country, he said there will not be a huge change and it will be done "step by step"
Minister for Transport Eamon Ryan says he expects plans to resume international travel from 19 July to be "on track". In relation to the further reopening of the country, he says there will not be a huge change and it will be done "step by step" | https://t.co/1bKdME63oe pic.twitter.com/HjLO5w3HpB— RTÉ News (@rtenews) July 6, 2021
Meanwhile, Minister for Public Expenditure Michael McGrath said the Government is anxious to see the resumption of indoor dining as quickly as possible.
"We are making real progress and I think with goodwill on all sides, we think we can get there quite quickly," he said at Dublin Castle.
Minister Michael McGrath says that the Government is anxious to see the resumption of indoor dining as quickly as possible. "We are making real progress and I think with goodwill on all sides, we think we can get there quite quickly," he says | https://t.co/1bKdME63oe pic.twitter.com/XhyHMuwgSM— RTÉ News (@rtenews) July 6, 2021
Separately, infectious disease specialist Professor Sam McConkey said discussion should now be taking place among decision makers in Ireland about "how much risk appetite" there is here in the reopening of society and the economy beyond the coming months.
Speaking on RTÉ's Today with Claire Byrne, Prof McConkey said "lots more variants" of Covid-19 are going to emerge.
He said a vaccine resistant variant could "wipe out" the vaccine bonus, and it would take three to six months before another vaccine would be created.
"My concern about international travel generally has been the arrival in Ireland of a variant that could transmit widely in vaccinated people or people who've had Covid before, and then our vaccine bonus which is very real, and tangible would be wiped out.
"Anywhere there is a lot of virus being transmitted in a partially vaccinated population allows the emergence and development and natural selection of a strain that could transmit in vaccinated people," he added.