The Ministry of Digital Government announced the release of two new applications. One is called Covid Free GR and its use seems to be very simple: to save a document in the wallet (which is the second application, you have to scan the QR code in the application, or upload it as a pdf file.
The "Save to wallet" option will appear immediately afterwards.
The Ministry of Digital Government states on the application page:
The official applications for verification and storage in the form of Wallet of European digital certificates COVID (EU Digital Covid Certificate) and national certificates COVID are available through the official account of the Hellenic Republic and allow them to be scanned, checked and saved.
The new application is available through covidfree.gov.gr as well as through the Apple App Store and the Google Play Store.