France previously staged the tournament in 1960 and were hosts again in 1984, winning it with a team captained by Michel Platini, the Uefa president.
The French, hosts and winners of the 1998 World Cup, beat Turkey by just a single vote after Italy were eliminated in the first round of voting.
Euro 2016 will feature 24 countries playing 51 matches over one month.
"This is a beautiful day for us," said Jean-Pierre Escalettes, president of the French Football Federation.
"It is a moment of intense emotion to know that in 2016 France will welcome European football and will fulfil its promises.
"What counts for us is to have the full confidence of Uefa and this trust will not be betrayed.
"We also understand the frustration of Italy and Turkey - particularly Turkey, who lost by a single vote after bidding for a third time."
French President Nicolas Sarkozy and former national team star Zinedine Zidane supported their country's case in a presentation to Uefa's ruling executive in Geneva on Friday.
The French government has pledged to help guarantee the projected 1.7bn euro (£1.45bn) cost of building and renovating stadiums.
The 2016 event will feature 24 countries for the first time, up from 16 in Euro 2012, which is being co-hosted by Ukraine and Poland.
France will become the first country to stage the European Championship three times.
No doubt Michel Platini, the head of UEFA, influenced this decision! They do have the stadiums and the infrastructure from the World cup in 98 though.


