The announcement will also give hope to Scotland, Wales, and the Republic of Ireland of hosting some Euro 2020 matches – they, too, have already expressed their interest to Uefa.
General secretary Gianni Infantino said: "Some important decisions have been taken. Uefa Euro 2020 will be staged across the continent, in various major cities. A Euro for Europe follows an initial idea by Uefa president Michel Platini.
"The response has been extremely positive from all the national associations."
Turkey had initially bid to host Euro 2020, and Infantino confirmed the country's Uefa vice-president Senes Erzik opposed the decision.
The bidding process for host cities will start in March.