Probably be a stamp in your passport.
The WHO is working to add proof of Covid vax to their internationally recognized Yellow Card. Those of us who travel to tropical Africa or Latin America already have them for yellow fever, dengue and typhoid fever vaccines required to enter those counties as has been for 25+ years now. This is the way it will be done in the world scale the WHO is also working on a QR code version of the yellow card as a means of mass distribution since paper cards take time and effort to distribute but nearly every traveler on earth has a smart phone with basic net access needed for a digital QR version.