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Barcelona's Argentina striker beat club team-mate Xavi Hernandez and Real Madrid's Cristiano Ronaldo in a poll of 53 sports journalists representing each of the Uefa member associations.
"I'd like to thank all the people that voted for me, and all my teammates," Messi said at the awards ceremony in Monaco.
"I keep all these awards at home and I still have some space for more. It's an honour to be so successful and to come up with the goods at the right time. Thanks to my teammates for helping me achieve this."
Messi, 24, scored scored 53 goals last season, including 12 in the Champions League, where he finished as the top scorer for the third season in succession, scoring in the 3-1 victory over Manchester United in the final.
Four Barcelona players were in the top 10, with Andres Iniesta fourth and Gerard Pique joint eighth.
Porto's Falcao was fifth, the Manchester United pair Wayne Rooney and Nemanja Vidic sixth and seventh, Zlatan Ibrahimovic of AC Milan alongside Pique in eighth and Germany keeper Manuel Neuer, who has moved from Schalke to Bayern Munich, 10th.
The award replaces the European Footballer of the Year award won in 2010 by Inter Milan's Diego Milito.
