"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."
Turkey had initially bid to host Euro 2020 and the country's UEFA vice-president Senes Erzik opposed the decision, Infantino confirmed. The format and number of cities that will be involved in the tournament will be decided by UEFA's national teams committee.
Infantino said the bidding process for the host cities would start in March and would take a year with decisions made in the spring of 2014.
UEFA also decided that the 2013/14 European women's under-17 tournament will be hosted in England.