Ribery earned 36 votes in the poll of journalists from across Europe -- 23 more than four-time reigning world player of the year Messi. Real Madrid forward Ronaldo won three votes.
"It's a very special moment to be standing here this evening," Ribery said after receiving the award following the draw for the group stage of the Champions League in Monaco.
The 30-year-old Ribery was instrumental to Bayern Munich's incredible season in which the team won the Champions League, Bundesliga and German Cup.
"This distinction rewards Franck for the magnificent season he had with his club and above all underlines his magnificent talent which allows him to be considered among the best players in the world," French Football Federation President Noel Le Graet said. "Everyone in French football is very proud, and are with me in congratulating him."
The three-man shortlist was selected by a panel of 53 journalists drawn from each of UEFA's member nations. The same journalists then voted for the winner.
UEFA created the award after France Football magazine combined its traditional European accolade with FIFA's world player prize. Messi won the inaugural prize in 2011 but was beaten by Barcelona teammate Andres Iniesta last year.
It is the third consecutive year that Messi and Ronaldo have been on the shortlist.