UEFA President Aleksander Ceferin announced on Thursday that England's national stadium would now host the three group stage games and one knockout match slated for the proposed new "Eurostadium" in Belgium.
FA chief executive Martin Glenn said: "We are delighted to help Uefa by hosting the additional four matches at Wembley Stadium".
Cardiff's Principality Stadium and Stockholm's Friends Arena - the venues for last season's finals of the Champions League and Europa League, respectively - had hoped to pick up Brussels' games.
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Wembley will now host a total of seven games for the 2020 Euros.
The building of a new Brussels stadium for the tournament had run into delays involving the applications for construction and environmental permits.
While the full schedule is still to be confirmed by UEFA, the Stadio Olimpico in Rome will stage the opening game.
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But the exclusion of Brussels means the 90,000-seater venue will also get group games and a match in the first knockout round.
It said that Group A would be played in Rome and Baku, Group B in St Petersburg and Copenhagen, Group C in Amsterdam and Bucharest, Group D in London and Glasgow, Group E in Bilbao and Dublin and Group F in Munich and Budapest. The Welsh football association was "extremely disappointed", saying it may have been their only chance ever to host a Euro or World Cup final.
UEFA said that each host nation that qualifies will play at least two matches at home in the group stage.
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"This has been a collective and collaborative process and we could not have done it without the support of the Government and the Mayor of London. Today we don't know if they can build a stadium or not", he told reporters at UEFA headquarters in Nyon.