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 Englisth Football Association will bid for Wembley to host the final while Wales and Scotland will also bid for Euro 2020 games, and it is expected Ireland will attempt to host matches in Dublin also.
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 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.
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."