England, which failed in the quest to host the 2006 and 2018 World Cups, was given the final by UEFA on Friday after Germany withdrew Munich's bid just before the vote.
"I know the party side of London, the way the English welcome people," UEFA President Michel Platini said. "Wembley will doubtless live up to the responsibility."
England hosted Euro '96 with the final at the old Wembley. The venue has since been rebuilt into a 90,000-capacity stadium, and staged two Champions League finals in the past three years.
Now the target for England, which lost to Germany in the Euro '96 semifinals at Wembley, is to ensure it reaches the last four again in 2020.
England's only title came on home soil, winning the 1966 World Cup final at Wembley.
"If we look backed historically in '66 it went very well for us when we hosted a tournament and in 1996 I thought we were very unlucky to lose the semifinal on penalties," England coach Roy Hodgson said. "Young players of today have got to be thinking this is a great opportunity for us to not only be a part of a wonderful tournament but maybe there at the end when the prizes are being dished out."
The new format gave an opportunity to stage some games to countries that wouldn't necessarily have a chance to host the tournament on their own.
Baku, the capital of Azerbaijan, was one of the cities awarded a quarterfinal match and three group games, along with Munich, Rome and St. Petersburg. Three group games, plus a second round match, were awarded to Dublin, Copenhagen, Bucharest, Amsterdam, Bilbao, Budapest, Brussels and Glasgow.
Dublin is the westernmost venue while the eastern extremity is Baku. Azerbaijan, which separates Russia and Iran along the Caspian Sea, is spending sovereign wealth to project a softer image through sport.
The UEFA vote came a day after Azerbaijan's human rights record was criticized by the European Parliament. Legislators called on the Azerbaijani authorities "to undertake long-overdue human rights reforms without further delay and cease their harassment of civil society organizations, opposition politicians and independent journalists and lift the ban of public gatherings in Baku."
But Platini defended the choice of Baku, which is building a 69,870-capacity stadium set to open next year.
"If we started to look at all these problems we wouldn't have football played throughout the world," Platini said when asked about criticism of Azerbaijan. "We are involved with football. Football is football, politics is politics."
Rob Harris can be followed at www.twitter.com/RobHarris