France, who staged the tournament in 1960 and 1984 and have also hosted two World Cups, beat Turkey and outsiders Italy in a UEFA vote.
"It is an answer of optimism, we will go through the economic crisis with economical, social, structural measures, but we will also go through the crisis thanks to the confidence a country has in itself and a great sporting event can contribute to that confidence," said sports minister Roselyne Bachelot.
France won the last two competitions they hosted, Euro 1984 and the 1998 World Cup.
"By choosing France, UEFA valued our country's ability to stage big international sporting events, to promote the values of sport and to welcome the supporters," Prime minister Francois Fillon said in a statement.
President Nicolas Sarkozy, who delivered a speech in Geneva before the vote, told reporters afterwards: "We will do our best so that the 24 nations are wonderfully welcome in France, we will start to work on the stadiums.
"I say to our Italian and Turkish friends that I feel sorry for them, they also built very very good files."
Hosting the Euro 2016 finals is also set to secure 15,000 extra jobs in the country, with 1.7 billions euros to be invested in the stadiums' renovation.
"We will do our best so a sporting spirit prevails, so that French people see something else than the crisis' gloom, it is important," said sports junior minister Rama Yade.
"There will also be economical repercussions because to build four stadiums, renovate eight, you need the building trade, the businesses."
Zinedine Zidane, who scored two of France's goals in the 3-0 World Cup final win against Brazil in 1998, told RTL radio: "I am delighted for the millions of French people who are going to share this."
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