Sports paper O Jogo gave its headline "Eternal" with a picture of the whole team.
"Sunday began with a jackpot of medals at the European Athletics championship and it ended with an explosion of heroics and happiness," the daily wrote.
The Record had a picture of the players with the headline "Epic", while another sports paper, A Bola, splashed an image of captain Cristiano Ronaldo lifting the Cup.
Ronaldo, who had his struggles in the tournament and left the final in the first half with a knee injury, did his part in helping the Portuguese in their famous run.
His two equalisers in a 3-3 draw with Hungary allowed them to advance from the group stage and also made him the first player to score in four editions of the tournament.
A tearful Ronaldo held the trophy in the Correio da Manha newspaper, which trumpeted: "The Euro is ours, we are the champions."
Online, Jornal de Noticias showed coach Fernando Santos lifting the Cup with the headline "It's ours!".
"Ronaldo lifted a Cup made up of effort and tears," the paper declared.
(Reporting by Adriana Garcia; Editing by Ian Ransom)
