France, who staged the tournament in 1960 and 1984 and have also hosted two World Cups, won the vote 7-6 at the expense of Turkey, who had been making their third bid for their first major soccer championship.
"Right now I'm overwhelmed just thinking that France will welcome the Europe of football," French Football Federation President Jean-Pierre Escalettes said at the televised ceremony.
"What matters to us is to have the trust of UEFA and that trust will not be betrayed."
France President Nicolas Sarkozy appeared at the ceremony to support his country's bid, sitting alongside the French president of UEFA, Michel Platini, who led his country to victory as an inspirational player in 1984.
Platini sat out the executive committee meeting which voted on the winners and admitted it was an uncomfortable situation for himself and vice-president Senes Erzik of Turkey, who also took a back seat.
"The position was rather complex, not just for the president but also for the vice-president. We had nothing to win in this situation," said Platini.
"This has proved the president is not a dictator because, if he was, the vote would have been 13-0."
Problems and delays in Poland and Ukraine, who will jointly host Euro 2012, may have persuaded UEFA's executive committee to avoid choosing Turkey, especially as 2016 will be the first tournament to feature 24 teams, expanded from the current 16.
The Turkish government had promised to invest one billion euros of public money in stadiums for the event. It would also have needed to spend some 20 billion euros on national transport infrastructure, including high-speed trains.
"We are devastated. This was our third bid so it is not much consolation to know that we lost by a small margin," Turkey's Euro 2016 bid manager Orhan Gorbon told Reuters in Istanbul by telephone.
"Losing is one thing but it is an underestimation of Turkey to say it was not capable of hosting a larger tournament, or it was to do with Ukraine...I don't understand why France should be seen as the safe option."
The French budget for stadiums is 1.7 billion euros, of which 39 percent will come from public investment. UEFA's review of the bids said around half of the required private funding had already been secured. The French proposal includes 12 stadiums, four of them new.
CRITICAL REVIEW
Sarkozy had told UEFA that France wanted to host the event because of, rather than in spite of, the worldwide economic problems.
"We asked ourselves whether we wanted to be candidates in the middle of a crisis," he said during the French presentation.
"But sport is an answer to the crisis. It is because we are in a crisis that we need sport. Nothing is more powerful than sport and, within sport, nothing is more powerful than football."
Italy's chances had been written off after a critical review of their bid following UEFA's inspection visits and it was no surprise to see them eliminated in the first round of voting.
