The programme will be rolled out across the rest of the 27-nation bloc on July 1.
Croatia, Denmark, Bulgaria, the Czech Republic and Poland are the other countries starting early, according to the European Commission.
Greece, which depends heavily on tourism, has been pressing for the commonly recognised certificate that uses a QR code with advanced security features.
The move comes as Brits gear up for the summer holiday season following the return of international travel in May.
Holidaymakers are hoping for destinations like the Greek islands to switch to the quarantine-free green list during the travel announcement on Thursday.
Who can get the EU vaccine certificate?
Certificates are being issued to:
Fully vaccinated people
People who have contracted the virus and developed antibodies
Others who have had a PCR test within the past 72 hours
How does the EU vaccine certificate work?
The documents will have both digital and paper forms.
They will be free of charge, distributed in the national language plus English and be valid in all the bloc’s countries.
A ‘crucial step’ towards safer travel
EU health commissioner Stella Kyriakides said: “EU citizens are looking forward to travelling again, and they want to do so safely.
“Having an EU certificate is a crucial step on the way,”
Greece’s digital governance minister, Kyriakos Pierrakakis, said easier travel will open up within the EU as nations adopt the new verification standard.
“What will happen is that countries will stop issuing certificates using their own convention and adopt the common convention,” Mr Pierrakakis told private Skai television.
“That will simplify things considerably, because you can imagine the number of bilateral agreements that would otherwise need to be worked out.”
What to expect
Mr Kyriakides said in the next few weeks, all EU nations need to “fully finalise their national systems to issue, store and verify certificates so the system is functioning in time for the holiday season”.
Countries will be allowed to add extra vaccines to their individual entry list, including those that have not been formally approved for use across the EU.
The European Commission believes that people who are vaccinated should no longer have to be tested or put into quarantines, regardless of where they are travelling to or from, starting 14 days after receiving their second jab.
Member countries, however, have not yet endorsed that recommendation.