The decision was announced following a meeting of UEFA's executive committee in Lausanne on Thursday.
UEFA general secretary Gianni Infantino told a press conference after the meeting: "Some important decisions have been taken.
"UEFA Euro 2020 will be staged across the continent, in various major cities, following a decision taken today. A Euro for Europe follows an initial idea by UEFA president Michel Platini.
"The response has been extremely positive from all the national associations."
The format and number of host cities that will be involved in the tournament, which will feature 24 teams, will be decided by UEFA's national teams committee with the bidding process to begin in March.
A final announcement is expected in the spring of 2014 with the Football Association having already put Wembley forward as a possible venue for the final.
FA chairman David Bernstein said: "Clearly Wembley is incredibly highly thought of by UEFA and it is something we will push for.
"UEFA want to hold the semi-finals and the final on the same ground, or in the same city and I think we would be on their shortlist - but there would be some strong competition.
"The public want it and we'd want it and it would be wonderful to have it here."
Wales and Scotland have also confirmed they will bid for matches - including a possible bid for a final in Glasgow to rival Wembley's - and the Republic of Ireland are also expected to follow suit.
Meanwhile, UEFA also announced that the 2013/14 European women's under-17 tournament will be hosted in England.
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