The showpiece fixtures were initially set to be attended by around 45,000 fans, but approximately 75 per cent of the ground will now be filled.
It will be the largest crowd assembled for a sporting event in the United Kingdom in 15 months.
Wednesday's (AEST) announcement comes a day after Italy's prime minister Mario Draghi called on UEFA to stage the games in Rome, while Budapest had been touted as another alternative.
However, the British government has struck an agreement with UEFA to ensure that all three matches will still be played at Wembley.
UEFA President Aleksander Ceferin said in a statement: "It is great news that so many fans will be able to watch the final three matches of Euro 2020 at Wembley.
"The last 18 months have taught us – both on and off the pitch – how integral fans are to the fabric of the game.
"This tournament has been a beacon of hope to reassure people that we are returning to a more normal way of life and this is a further step along that road.
"I am grateful to the Prime Minister and the UK Government for their hard work in finalising these arrangements with us, to make the tournament final stages a great success."
The semi-finals will be held on July 6 and 7, while the final is set to take place on July 11.
All ticket holders must show a negative COVID-19 test or proof of full vaccination two weeks before the games they attend.
It had previously been confirmed last week that 40,000 fans can attend the last-16 match staged at Wembley between Italy and Austria on Saturday.
Football Association chief executive Mark Bullingham said: "It is great that the Government has agreed to allow over 60,000 fans in Wembley for the final three matches of the tournament.
"It's amazing how much atmosphere fans have been able to generate so far, so to have three times as many will be fantastic.
"We have always said that fans are the lifeblood of the game, so it's brilliant that so many will get a chance to see the tournament finale.
"We hope that this programme lays the foundation for the safe return of fans in stadiums all across the country next season."