Oyarzabal finished off a swift counter-attack for the winner after England had fought back from a goal down for the fourth successive match and seemingly earned extra-time.
"I have done my job," said Oyarzabal, who came on for captain Alvaro Morata after 67 minutes. "Just the fact of being in the 26, you value it a lot. It happened to me but could have happened to anyone."
Spain manager Luis de la Fuente added: "I couldn t be happier. A real team, European champions. I said I was proud and today I am even prouder. It confirms what we are. For me, they are the best in the world."
After a cautious first half where Spain had 65% possession but England s Phil Foden managed the only shot on target, the Spaniards struck two minutes after the restart, despite losing influential midfielder Rodri to injury at the break.
Teenager Lamine Yamal, who had been shackled completely in the first half, finally found space down the right and crossed for Nico Williams to slot home past goalkeeper Jordan Pickford.
Spain then enjoyed a purple patch with a series of sharp attacks as England s previously watertight defence lost its shape and Dani Olmo, Morata and Williams all had good chances.
England manager Gareth Southgate sent on Ollie Watkins, the scoring substitute hero of the semi-final, for an ineffective Harry Kane after an hour, with Cole Palmer, England s most creative player in the last month, joining him 10 minutes later.
PAY OFF
The changes paid off almost immediately when Jude Bellingham laid the ball back into Palmer s path and the substitute curled home a precise low 20-metre shot in the 73rd minute.
The massed ranks of England fans, who vastly outnumbered their rivals, exploded and the whole feel of the night changed.
But Spain weathered the storm and a lapse of concentration saw England undone as Marc Cucurella was left in space on the left, received the ball from Oyarzabal and drilled it across the box for the substitute to stretch out a toe and poke it home.
There was still time for more drama as Spain keeper Unai Simon parried a Declan Rice header from a corner and Dani Olmo then brilliantly headed away Marc Guehi’s follow up on the line.
It meant that Spain added a fourth title to those won in 1964, 2008 and 2012 and, as only the third team in the last nine Euros to win the trophy without coming through a shootout at some point in the tournament following France (2000) and Greece (2004), nobody can deny they were worthy winners.
For England the "30 years of hurt" after their 1966 World Cup success, which was the soundtrack to their hosting of Euro 96, will now run to at least double that number as they became the first team to lose successive Euro finals
"We ve competed until the very end of the final," said Southgate, who is widely expected to step down having remarkably led his country to two Euro finals and World Cup semi and quarter-finals in his eight years in charge.
"I think we didn t keep possession of the ball quite well enough. They press you really well and you ve got to get out of that pressure and we weren t able to do that and in the end that meant they had more control of the game
"The players have got to take enormous credit for getting us to the point they did. They way they fought and represented the shirt with pride. They were never beaten until the very end, the final five minutes of the last game and then that chance at the end. Just the character and resilience that they ve shown.
"It s fine margins, but I think they (Spain) were the best team in the tournament and they deserved to win."
