European football's governing body announced the move on Thursday, saying it would allow smaller countries a slice of the action as they would not be able to stage an unwieldy, 24-team tournament on their own.
The event is being increased from 16 to 24 teams for the 2016 edition in France and UEFA said the format would help to ease the burden on host nations, although it is a one-off move to celebrate the tournament's 60th anniversary.
European Club Association boss and Bayern Munich CEO Karl-Heinz Rummenigge was upbeat about the move given the dire effects of the euro zone financial crisis across the continent.
"At this time of a united Europe, I consider this to be a good decision. At a time of euro crisis one or two countries should not be forced to invest in infrastructure projects but instead existing structures should be used," he said.
Fernando Gomes, head of the Portuguese Football Federation (FPF), praised the idea and said he hoped UEFA would take Portugal into consideration for hosting matches given that they already had infrastructure in place after Euro 2004.
"We congratulate them on the idea. In a period of great financial difficulties there is no doubt that this idea is welcome," said Gomes.
"This decision gives Portugal the opportunity to welcome Euro 2020 matches in one city or another or in one stadium or another that we built for Euro 2004. We are sure UEFA recognises the FPF's capacity to organise big events and I am sure they will take us into consideration."
German Football Association (DFB) president Wolfgang Niersbach joined in with the positive feedback and said his country would bid with one city.
"We expected such a...decision and we think it is an absolutely positive one. It is now the job of the federations commission, of which I am also part, to further develop the 2020 concept," said Niersbach.
"One thing I can say today is that we will be bidding with one German city."
England, Scotland and Italy have expressed interest in hosting matches, with the FA proposing Wembley Stadium in London as a potential venue for the final though they will face competition from Scotland.
"We would be interested in the final but we first have to find out UEFA's minimum criteria for capacity," said Scottish FA chief executive Stewart Regan.
Scotland boasts the 60,000-plus-seater Celtic Park and the 50,000-plus Ibrox and Hampden Park stadiums in Glasgow though they are small in comparison to Wembley's capacity of more than 80,000.
Italian Football Federation (FIGC) Giancarlo Abete said Rome and Milan could stage matches.
"Rome hosted a Champions League final not so long ago, and Milan should have one assigned to it by the Executive next March," Abete was quoted as saying by ANSA news agency.
"Italy is ready to host the 2020 European Championship, Rome and Milan are great cities capable of hosting such an important event."
Arsenal manager Arsene Wenger described UEFA's bold plan as "creative" and said he was not against it, yet the Frenchman had some doubts.
"The advantage is that the whole of Europe would be concerned by the championship," Wenger told reporters on Friday.
"The disadvantage is sometimes when the country organises the European Championship, it's a good opportunity for them to build structures that are very useful: new stadiums, new training pitches and new communication facilities.
"It's always a good opportunity to make up-to-date structures for football. In the long-term that's important."
In Russia, local media noted that Moscow had been included in a list of possible host cities though mos
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