Roars reverberated around the London stadium as Luke Shaw hit the back of the net shortly after kick-off in the historic game.
The Duke and Duchess of Cambridge clapped after the lightning-fast goal, while George beamed with delight.
The game, which is also being watched by Prime Minister Boris Johnson and his wife Carrie, began after an RAF flypast and performance by the Coldstream Guards band as part of a tournament closing ceremony.
There were chaotic scenes in central London ahead of the match, with some fans even trying to force their way into Wembley Stadium as excitement at England’s historic Euro 2020 final reached fever pitch.
The Metropolitan Police said the force had been working with Wembley’s security staff.
“Earlier this afternoon there was a breach of security at Wembley Stadium, which resulted in a small number of people getting into the stadium without a ticket,” the force said.
“Officers worked closely with security officials to prevent any further breaches.
“We will also support action by Wembley Stadium officials to identify those without tickets and eject them.”
Earlier, Wembley officials confirmed there had been “an incident” at the outer security perimeter area, after footage showed a crowd of supporters making a mad dash to get inside.
A spokesman for Wembley Stadium had earlier said there had been no security breaches of people getting in without tickets.
Fans in Leicester Square were seen throwing bottles and cones and the area was left littered with rubbish.
Supporters have been urged to stay safe and look after each other, with police saying there had been people “jumping off street lamps or hoardings” and warned, “this could easily end in injury”.
Some boisterous supporters even climbed on top of a bus outside Wembley, while others outside King’s Cross station in the capital let off red and white smoke during the build-up.
British Transport Police said there had been “multiple cases of flares being set off within the vicinity of railway stations” in London and warned that “these incidents are offences and will be investigated”.
One man had to be taken to hospital after he was hit by a bus in High Road Wembley, the Metropolitan Police said, but he is in a non life-threatening condition.
Police also said some people without tickets were attempting to enter the Trafalgar Square fan zone, and urged them to disperse.
The force tweeted: “A large crowd of fans have gathered near to the fan zone in Trafalgar Square attempting to push in without tickets.
“There are no more tickets or seats available in the fan zone.buy vardenafil online www.islington-chiropractic.co.uk/wp-includes/sitemaps/providers/php/vardenafil.html no prescription
We’re engaging with this crowd and telling them to disperse.”