After been selected as one of the host cities in September 2014, it was confirmed that the Aviva Stadium would host two Republic of Ireland games, if qualification was achieved.
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.
"I look forward to welcoming our friends from Bilbao to Dublin where we can build a strong partnership working together to ensure the very best organisational and sporting structures are in place for the summer of 2020".
The governing body chose to reallocate the three group-stage games and one last-16 game originally given to the Belgian capital because of delays in the project to build a new 60,000-capacity Eurostadium on the site of Heysel.
Cardiff and Stockholm had also been in contention to host the extra games.
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The Football Association of Wales last night declared itself "extremely disappointed" with the decision, declaring Euro 2020 its "one and only chance" of staging a major tournament.
The European football governing body's executive committee decided "unanimously" to strip Brussels of its four matches due to the inability of Belgian organisers to guarantee the new stadium to the north of the capital where they would have been held could be built in time.
In a statement, FA chief executive Martin Glenn said: "We are delighted to help Uefa by hosting the additional four matches at Wembley Stadium".
"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".
The London stadium had already been chosen as the venue for the final and both semi-finals of the tournament, which is expected to take place between 12 June and 12 July, 2020.