It will be the first time since Euro 96 that a major men’s football tournament has been held in England and Wembley’s bid was confirmed at a UEFA meeting in Geneva after Germany withdrew Munich’s rival bid just before the vote.
Hampden Park in Glasgow and Dublin’s Aviva Stadium will both stage three group games and a last-16 match, but there was bitter disappointment for the Welsh after Cardiff’s bid was beaten by a single ranking point by the Scots.
Hodgson said England had benefited hugely when it had previously hosted the 1966 World Cup and Euro 96.
He said: “It’s a great reward for a lot of hard work which has gone into achieving this success. It is a major honour and great boost for us.
“If we look back historically in ‘66 it went very well for us when we hosted a tournament and in 1996 I thought we were very unlucky to lose the semi-final on penalties and we could quite easily have gone on to win it with Terry Venables’s team.
“Young players of today have got to be thinking this is a great opportunity for us to not only to be a part of a wonderful tournament but maybe there at the end when the prizes are being dished out.”
UEFA is staging the tournament in 13 cities across Europe to mark the 60th anniversary of the first European Championship. The quarter-finals and three group matches will be held in Munich, Baku, Roma and St Petersburg.
The other host cities, which will hold three group games and a last-16 game, are Copenhagen, Bucharest, Amsterdam, Bilbao, Budapest and Brussels.
Germany withdrew Munich’s bid just before the vote in order not to harm their chances of winning the right to host the entire Euro 2024 tournament, leaving the field clear for London.
Football Association chairman Greg Dyke said: “We are delighted – it’s nice to win one! Wembley is a great stadium and we are delighted to be holding the finals of this tournament.
“Wembley has been completely rebuilt since 1996 and it is a wonderful stadium.”
Dyke also praised UEFA for the idea of hosting the tournament across 13 cities in Europe and said hosting the final would be “a great incentive” for the England team.
He said: “We would love to host the finals and semi-finals but we would also like to be there.
“Some of the current players will still be around in 2020 and this will be a great ambition for them to take us to Wembley. It is a great incentive.”
UEFA president Michel Platini said that Wembley would live up to expectation.
He said: “I know how London can throw a party and the way the English welcome people. London will be up to the responsibility of hosting three exceptional matches in an extremely well-known stadium.
“We know it very well after two Champions League finals and now it will receive the cream of the crop of European football.”
The group game hosts will be guaranteed to play at least two games at home – if they qualify –but England’s group matches will be down to the luck of the draw, and they could even be drawn to play in Scotland. England will also have to qualify for the tournament.
Dyke added: “I’m not sure we would have fancied playing in Glasgow on Thursday night but we would have no problem playing in Scotland or Ireland.
“If that’s where we play then that’s where we play, that’s football.”
Wales are now expected to target hosting a Champions League final at the Millennium Stadium before 2020.
Football Association of Wales chief executive Jonathan Ford said: “We are bitterly disappointed.
“But on the technical side we could not have put in a better bid.”
“We have always talked to UEFA about other events and certainly I would hope with so many cities being used in 2016, 2018 and 2020 there will be other cities chosen to stage major events and that Wales will have one of those.”
John Delaney, the chief executive of the Football Association of Ireland, said staging European Championship matches would be a huge boost to the sport in the country.
Delaney said: “We put in a very good technical bid, we knew that and scored very well in the ranking.
“It means everything to football in Ireland. It will be the biggest field sport event that will ever come to our country.
“Years ago no-one thought we could do something like this – we would never have dreamt it.”
How the games for Euro 2020 will be allocated.
Final and semi-finals: Wembley Stadium, England
Three group gamesz and one quarter-final: Baku, Azerbaijan; Munich, Germany; Rome, Italy; St Petersburg, Russia.
Three group games and one last 16 match: Dublin, Republic of Ireland; Glasgow, Scotland; Copenhagen, Denmark; Bucharest, Romania; Amsterdam, Holland; Bilbao, Spain; Budapest, Hungary; Brussels, Belgium.