"When we are very good, we're the best of the best. Congratulations Salvador Sobral," President Marcelo Rebelo de Sousa wrote in a message to the 27-year-old crooner.
A cheering crowd thronged Lisbon airport to welcome him and his older sister Luisa Sobral, who wrote the winning song. They were escorted through the crowd by police.
"Salvador! Salvador! Portugal!Portugal!" they yelled as the triumphant singer shyly waved to them, holding a bouquet of roses in one hand.
"This prize is going to trigger a certain madness about me but I know it is short-lived," he said at a brief press conference. "What interests me is making music with meaning."
Fans meanwhile showered praise.
"It was a well deserved win, with a song that was different from all the others," said Pedro Antunes, a 29-year-old musician who follows the contest every year.
Maria Amorim, 49, held up a poster proclaiming: "Salvador, you have fulfilled my childhood dream" that Portugal would one day win the contest.
"A page of history has been written in Portuguese this evening at Eurovision. Bravo Salvador! Bravo Portugal," Prime Minister Antonio Costa tweeted.
'Dancing naked ape'
The singer stirred the professional judges and the public in the 60-year-old contest with a melancholic rendering of "Amar Pelos Dois" (For the Both of Us), sung in his native tongue.
Most contestants sing in English at Eurovision which draws around 200 million television viewers.
Sobral's quietly sensitive performance set it apart from the more flashy displays, such as the bookmakers' favourite Italian Francesco Gabbani and his "dancing naked ape" as well as Azerbaijan's entry which featured a man on a stepladder wearing a horse's head.
His decision to forgo the elaborate choreography and heavy dance tempos favoured by most contestants had made Sobral, a fan of trumpeter Chet Baker, a long shot to win.
Sobral's heart condition means he cannot go anywhere for more than two weeks without his medicine, and he did not attend earlier rehearsals in Kiev because of health worries.
But he plays down his heart ailment, even though he is still waiting for a transplant.
"The disease is a small problem, really, certainly the only one I have in my life."
The singer hailed his win as a "victory for music".
"This is a vote for people who actually mean something with their music," he said following his victory in Ukraine on Saturday night.
"Music is not fireworks, music is feeling. So let's try to do this and bring music back," he added.
#Salvadorable
Thrust to fame in 2009 with the Portuguese television show "Idolos", the country's equivalent of "American Idol", Sobral struggled with the sudden media exposure, even halting his singing career for a while.
Eight years later, and following a spell of heavy drug use, Sobral captured the hearts of scores of fans with a victory that surprised many, even if it was predicted by bookmakers.
Hundreds of fans in Portugal and around the world used the hashtag #Salvador or #Salvadorable to express their admiration for the "simple" and "talented" singer.
Even before the end of the competition, Brazilian singer Caetano Veloso had said Sobral deserved to win because he was simply "too good".
The Portuguese press amplified the singer's victory, in a country which has never managed to improve on its 1996 sixth place ranking at the Eurovision contest.
On an otherwise thin news day, Sobral made a front-page splash Sunday alongside a visit by Pope Francis to the Catholic site Fatima that drew a crowd of 500,000 and Benfica's 36th triumph in the country's national football championship.
As Benfica fans celebrated the team's fourth consecutive league championship on Saturday night, the jubilant scenes were briefly interrupted by Sobral singing on the gigantic speakers set up in the heart of Lisbon, the Eurovision champion's home town. tsc/ach/pvh
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