As a result, millions of Britons feared being banned from the island as AZ vaccines manufactured at the Serum Institute of India (SII) do not qualify.
However, Madeira - who have been put on the UK’s green list - said people who have received other vaccines can still visit.
Pedro Ramos, Madeira’s health secretary, said all would be accepted "because if millions have been vaccinated with these vaccines (not approved by the EU), their level of protection is similar to others".
Britons can check whether they had the SII jab by looking at their batch number which appears on vaccination record cards.
Those who were administered the Indian-made AZ vaccines will have the numbers 4120Z001, 4120Z002 or 4120Z003.
The EU’s coronavirus passport scheme allows citizens to show they have been inoculated, have tested negative for Covid or recently recovered.
This will help travellers move freely through different countries without having to quarantine or undergo more coronavirus tests.