Fully vaccinated people will begin receiving their EU Digital Covid Certificates from today.
One million certs issued via email will be sent to people who were vaccinated via the Health Service Executive portal.
Another million will be posted to those who were vaccinated in other settings, such as at their GP, and should arrive by the end of this week.
The certificates have a QR code, which contains encrypted data on a person's vaccination status obtained from the HSE.
Those who have recovered from Covid-19 in the past six months can apply for a Certificate of Recovery from a dedicated helpline, which Minister of State Ossian Smyth said he hopes will be operational by 19 July.
Once an application for a recovery cert is made, it will take up to five working days for it to be processed.
The third way of receiving a EU Digital Covid Cert is through a negative PCR or antigen test.
A number of private providers are linked to the Government system to allow them to issue QR codes to indicate a negative PCR test result, while a number of approved pharmacies have similar access to issue QR codes for a negative antigen test.
Each country has an app to read the QR codes, but travellers should ensure that they are familiar with the entry requirements of the country they are travelling to.
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The codes will be checked by airlines on departure from Ireland.
On the return or entry into Ireland, Department of Justice officials in ports and airports will carry out spot checks for the certs, which means not every code will have to be scanned.
Those who receive their EU Digital Covid Cert as a hard copy in the post can take a photograph of the certificate to carry on their phone, but they are advised to keep the printed copy in the event there is any issue with the image.
Information on the entry requirements for EU countries can be found on the Re-open EU website.
Minister for Justice Heather Humphreys said that increased resources will be put in place at border controls to carry out random checks for the certificate from travellers entering Ireland from the EU.
Speaking on RTÉ's News at One, Ms Humphreys said that random checks are "appropriate and safe" as all travellers will have been checked for the certificate before boarding a flight in the EU.
She said "we have to be practical" and are working to streamline the system of Covid certificate checks along with passport checks.
The EU Digital Covid Certificates will be checked by carriers at the point of Departure and random checks will be carried out on those entering Ireland with the certs.
Passengers are being warned that this could take extra time and that they should be prepared for their journeys to take longer.
Conor Cleary, Director of Operations, Border Management Unit, Dublin Airport said: "People should factor in that it will take a little bit longer to get through our aisles. We're going to be doing spot checks. It is going to add to transaction times per passenger. So if you can just factor that in before you travel, that it may take a little bit longer than the last time you travelled pre pandemic"
It will still be possible to travel in Europe without an EU Digital Covid Certificate
Existing proof of vaccination and testing will still be accepted but it could take longer to process
The government is currently only issuing vaccination certificates to those who were vaccinated by the HSE
It says Irish citizens who've been vaccinated in Northern Ireland, the UK or the US can travel on existing documents that prove they've been fully vaccinated and they will not be required to isolate
Minister Smyth said the government will "look at" issuing EUDCC's to Irish people who were vaccinated abroad in a later phase of the roll out of the cert
As travel rules throughout Europe continue to change, the main message to passengers is to check the entry requirements for the country they're travelling to before departure