This took me some time to find how to change the address using the online portal for the Portal das Finanças (Finance Portal) of Portugal. Writing them below for future references.
Finanças Index Page |
To change address:
You will receive the confirmation code by post to the new address in 5 days. Once you have received the code by post, to confirm the change address, visit the index page:
If you have any specific questions or require assistance, I recommend you contact them online using their support system, known as e-Balcao.
They are quite helpful, although they may take as long as a month to reply based on the time of the year. They get quite busy during the tax filing season. It helps if you ask your question in Portuguese though - even with the help of Google Translate, if you could not find someone who can speak Portuguese to help you.
Update as of 2021 January: From a comment below, I learn that the new link is, https://sitfiscal.portaldasfinancas.gov.pt/pessoal/morada/alterarMoradaSingularesForm1 Please use this link if the above links do not work anymore. I do not live in Portugal currently. As such, I am unfortunately not up to date with these latest changes.