The Ministry of Digital Governance announced the launch of two new applications. One is called Covid Free GR and its use appears to be particularly simple: to save a document to wallet (which is the second app, you need to scan the QR code in the app, or upload it as a pdf file.
Immediately after that will appear choice "Save to wallet".
The Ministry of Digital Government states on the application page:
The official applications for verification and storage in Wallet format of EU Digital Covid Certificates and national COVID certificates are available through the official account of the Hellenic Republic and enable scanning, control and their storage.
The new application is available through covidfree.gov.gr as well as through the Apple App Store and the Google Play Store.
Download the verification application | Download the Wallet app | Instructional video | Space signs - COVID-free badges