President Platini said UEFA had held talks with fans group Football Supporters Europe and convinced it that the "zany" format of holding games in 13 matches across Europe would benefit the majority of supporters.
The Football Association will bid for Wembley to host the final while Wales and Scotland will also bid for Euro 2020 games.
Platini told reporters at a briefing in Nyon: "We have talked to the fans. They were against it originally but we told them we are going to help them and suddenly they had a much more positive attitude.
"Certainly it will be easier for the English to go to Wales and Scotland to watch a match instead of having to travel the world. We have some decisions to make now - some political, some geographical - for example we cannot have an English fan going to Lisbon, Kazakhstan and Sweden.
"We will have an intelligent solution - not chasing the fans all over Europe.
"The Euros are coming to the fans and taking matches to quite a number of countries.
"We have met with supporters' associations recently and have reassured them we will do whatever is possible to make sure fans get the necessary support when they travel."
Platini himself came up with the idea of staging the tournament but he said it had been supported by every European country apart from Turkey, who had hoped to host the Euros on its own.
He added: "I just bring forward ideas and then national associations have their own meetings and workshops and 52 out of 53 said yes, I don't decide, the national associations have decided.
"Poland and Ukraine was a great Euro but it was very expensive, almost as expensive as the Olympic Games. It is perhaps a bit of a zany idea but it is a good idea."
Platini added that he wanted the finals and semi-finals to be in one city - and the FA will put London forward as a candidate.
He said: "I'm in favour the final phase being in one city to give it more importance, that's my idea. The executive committee will decide whether it's a good or bad idea."
"I think this would create a very special atmosphere among the supporters and it will be a week of national teams and it could be a great party."
Platini said FIFA president Sepp Blatter had congratulated him on the Euro 2020 idea - and that he is succeeding where the late Libyan leader Muammar Gaddafi failed.
Gaddafi had suggested moving the African Nations Cup around the continent, and Platini said: "I got congratulations from the president of FIFA, he said it is a marvellous idea. He said somebody wanted to do it a few years ago with the African Nations Cup and it was Gaddafi."
He also hit back at criticism from FIFA general secretary Jerome Valcke pointing out that the world governing body had ratified Japan and Mexico playing in South American competitions.
"FIFA accepts Mexico and Japan taking part in the Copa America and that is much more against the spirit than what we are suggesting," said Platini.
The UEFA president also insisted he wants to support the Europa League rather than scrap it - an interview he gave to a French newspaper last week led to reports UEFA are considering getting rid of the tournament and having a 64-club Champions League.
He added: "All I said is that there is a reflection going on to figure out what shape we want - we are discussing it, nothing is decided.
"I never said I am going to stop the Europa League. We have to look at all 53 countries and I believe the Europa League is great and that we need to support it and continue with it. It is a very popular competition.
"I am never going to organise competition for money's sake, only in the interests of football."