Platini, 51, defeated the Swedish incumbent Lennart Johansson, 77, by 27 votes to 23 in a poll of national Football Association presidents at the UEFA Congress.
Johansson had been in charge of European soccer's governing body since 1990.
Platini, three times former European Footballer of the Year, becomes the first high profile former player to hold such an important position in soccer administration.
He said after his victory: "I am moved, enormously moved but I am happy...it's the start of a great adventure."
Platini, who plans to cut the number of Champions League places open to the big national leagues, had used his final speech before the vote to put the emphasis on soccer's importance as a sport rather than a business.
"Football is a game before it is a product, a sport before it is a market and a show before it is a business," Platini told the Congress on Friday.
Platini also said before the vote that if successful he would propose Johansson should be appointed as honorary president to continue his work.
Platini was one of the most gifted players in the game's history. In 1984 he led France to victory at the European Championship, scoring nine goals in five games, and he was named European Footballer of the year three times.
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After playing for Nancy, St Etienne and Juventus, he retired in 1987 and the following year took up his first post within UEFA, as a member of the technical development committee.
He was a co-organiser of the successful World Cup in France in 1998, the year in which he became a personal adviser to FIFA president Sepp Blatter, who in turn endorsed him in the UEFA presidential election.
Platini pledged during the campaign to limit the number of places in the Champions League to a maximum of three, even for the major powers like England, Italy and Spain.
Otherwise there was little difference between the two campaigns, with both candidates promising to intensify the fight against racism, doping, match-fixing and illegal betting.
The lack of major contention between the two meant the fight was largely a friendly one, at least until the intervention of Blatter, who gave his public support to Platini on the eve of the election in a move that infuriated Johansson.
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