Real Madrid forward Ronaldo was carried off in tears in the 25th minute at Paris' Stade de France, eight minutes after injuring his knee in a clash with France's Dimitri Payet.
France, the firm favourites, were unable to capitalise on Ronaldo's absence, although they almost won it at the end of normal time when substitute Andre-Pierre Gignac turned and hit the inside of the post.
Raphael Guerreiro hit the bar with a free-kick for Portugal after 108 minutes, but seconds later they were ahead when Eder fired a low, 25-yard drive past keeper Hugo Lloris.
Ronaldo, who had given his Portugal team-mates animated encouragement in the break before extra time, was offering as much tactical advice as coach Fernando Santos in chaotic closing moments - and he was reduced to tears once more at the final whistle before lifting the trophy that has eluded his country for so long.
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Ronaldo's agony and ecstasy
Ronaldo has claimed the game's major prizes - such as the Champions League with Manchester United and Real Madrid - but a landmark victory with his country has always eluded him.
The greatest disappointment was when, as hosts of Euro 2004, Portugal were beaten 1-0 by rank outsiders Greece in the final at Lisbon's famous Stadium of Light.
Portugal also lost in the World Cup semi-finals in 2006, the quarter-finals at Euro 2008 and the semi-finals at Euro 2012 - and it looked like the curse would strike again when Ronaldo lay on the turf distraught after two attempts to play on through the pain.
What a contrasting image it was in the closing seconds of extra time as he virtually took charge of team affairs and light-heartedly bumped into coach Santos, before breaking down in tears when British referee Mark Clattenburg signalled full-time.
Ronaldo, with his knee heavily strapped, then hobbled up the steps to lift the Euro 2016 trophy and fill a gap in his glittering list of honours.
He was then centre stage in the subsequent celebrations, lying on the floor in front of his joyous team-mates.
The 31-year-old's night started and ended in tears, but this was a journey from agony to ecstasy - and his status as a Portuguese national hero was cemented even further.
Durable Portugal get the job done
Portugal may have been unspectacular winners of an unspectacular Euro 2016 - they won only one game in 90 minutes.
But this tough, resilient, organised team under coach Santos were justified in the wild celebrations that took place in front of their fans at Stade de France after the trophy presentation.
They finished third in their group, edged out of second place by Iceland's last-minute winner against Austria, a result that led to England's downfall in the last 16.
Portugal saw off the talented Croatia in extra time in the last 16, beat Poland on penalties in the quarter-finals and then ended the great Wales adventure with a 2-0 win in the semi-finals.
Every quality that kept them in contention - but never earned the plaudits - was on show here as they inflicted on France what Greece had inflicted on them at Euro 2004.
With goalkeeper Rui Patricio heroic and defenders Pepe and Jose Fonte outstanding, they frustrated France, growing in threat and strength as a largely tedious final ran on.
This was the greatest moment in Portugal's football history and the celebrations were worthy of the occasion.
Heartbreak for hosts France
France went into this Euro 2016 final backed by a tide of emotion and expectation after victory against World Cup holders Germany in Thursday's semi-final in Marseille.
Goalkeeper Lloris, one of France's senior figures, spoke of how Euro 2016 had helped the population "escape" the suffering of the Paris attacks in November, in which 130 people died and hundreds more were injured.
France's players have been dignified and carried that burden confidently to reach the final against Portugal, but there was to be no happy conclusion to this campaign as they failed to reproduce the form that beat Germany.
Perhaps that weight was finally too much for them here with the nation behind them. They were unable to take advantage of what should have been a huge lift to their hopes when Ronaldo went off - indeed his departure seemed to effect the hosts more than Portugal.
Gignac almost provided a dramatic winning goal in the final seconds of normal time, but in the final reckoning Didier Deschamps' side were unable to rise to the occasion and suffered the bitter disappointment of defeat in a major final in their own capital city.
Invasion of the moths
The Stade de France was invaded by moths in the hours before kick-off, making life uncomfortable for fans, players and officials.
Floodlights were left on at the stadium the night before the game, attracting moths who were still there when the teams and supporters arrived.
France coach Deschamps, referee Clattenburg and his team, plus players in the warm-up were under siege, swatting them away while staff in the stadium used brushes to attempt to get rid of the insects.
And in an image that was seen around the world, a moth landed on Ronaldo's face as he sat in tears on the turf after succumbing to a knee injury only 25 minutes into the Euro 2016 final.
What they said
France boss Didier Deschamps: "The disappointment is there and it's immense. There are no words to describe this feeling.
"Clearly we had our chances but we weren't cool-headed enough. My players gave everything tonight but unfortunately we lacked what is essential. We have to try and digest this.
"There is no way of reducing their disappointment, but we must not forget the enthusiasm of millions of people which our run generated. It is hard to look at the positives now but there are many.
"We did not play with the brakes on but Portugal are good at stopping you from playing. They play as a unit. Without Cristiano Ronaldo they had one fewer attacking option.
"We didn't play a bad game. We went for it."
Portugal boss Fernando Santos: "First of all I'd like to thank God for being with us, my wife, my mother, my grandson. My father wherever he is, he's probably having a few beers.
"Cristiano Ronaldo is an amazing example. Today he tried to remain on the pitch. He was very strong in the locker room, he helped all of the boys, that's the definition of teamwork.
"We have a bright future but right now we need to celebrate."
Former England captain Alan Shearer, speaking on Match of the Day: "Portugal set their system up and said, 'this is how we'll play, come and try to break us down'. It was a brilliant goal to win it, he was big and strong. The finish was sublime."
Former England midfielder Danny Murphy, speaking on Match of the Day: "It's an amazing story for a team who weren't fancied before or during the tournament.
"Portugal have shown they possess character and quality. Tonight they didn't need Cristiano Ronaldo. People won't remember he didn't play much tonight, they'll remember he captained them to their first major trophy.
France 1998 World Cup winner Thierry Henry, speaking on Match of the Day: "It's a sad day. We have a lot of Portuguese in France. We'll hear about this for a looong time.
"You can only win a tournament as a team - perfect example, Ronaldo comes out and Portugal win it. It was like, 'let's do it for him'."
The final in numbers
35: Portugal have won their first European Championship after 35 games at the tournament.
10: They are the 10th different nation to be European champions.
6: Eder is the sixth substitute to score in a European Championship final, along with Oliver Bierhoff, Sylvain Wiltord, David Trezeguet, Juan Mata and Fernando Torres.
3: Portugal become the first team in European Championship history to go to extra time three times in the same tournament.
80: They took until the 80th minute to register a shot on target, the longest wait for a team in a European Championship final.
Source: bbc.com