Although members of the European Union automatically have the right of residency in Portugal, all foreigners have to register with the “Serviço de Estrangeiros e Fronteiras” (Foreigners and Border Service). You should also say hello to your local Consulate. It may come in useful in the future and you might get nice invitations!
Then there is your fiscal residency to be considered. Residency status requires some paperwork; we shall take you through the process.