Along with Messi, who was named the best footballer in the world, Modric was joined by Liverpool goalkeeper Alisson, who was also named the world's best goalkeeper, Matthias de Ligt (Juventus), Marcelo (Real Madrid), Sergio Ramos (Real Madrid), and Virgil van Dijk (Liverpool) in the defense, midfielders Frenkie de Jong (Barcelona) and Eden Hazard (Real Madrid) and strikers Cristiano Ronaldo (Juventus) and Kylian Mbappe (PSG).
Argentina and Barcelona forward Lionel Messi is presented with the men's player of year award by FIFA President Gianni Infantino.
His club manager Jürgen Klopp was named coach of the year after steering Liverpool to the Champions League title in June, while teammate Alisson won the best men's goalkeeper award.
Van Dijk had been bidding to become a rare defender to win a Federation Internationale de Football Association player award, since Italian Fabio Cannavaro won the World Player of the Year, and he Ballon d'Or in 2006.
In the women's category, Rapinoe claimed the top award after helping her country to back-to-back World Cup titles this year.
Rapinoe scored six goals in the tournament, earning her the Golden Boot for the tournament's top scorer and the Golden Ball as the top player.
Police use tear gas in Paris amid array of protests
By 1 pm, 106 demonstrators had been arrested, police said, adding that some had been found to carry hammers or petrol canisters. But anger is now mounting again over his plans to overhaul France's costly, convoluted pension system .
"The people who vote made a decision and you have to accept it".
"We have incredible platforms, the unique opportunity to use this to actually change the world for the better".
Klopp won the award ahead of Manchester City boss, Pep Guardiola and Tottenham coach, Muaricio Pochettino.
"As a coach you can only be as good as your team".
"The World Cup really was a showcase, the world fell even more in love with the game", said 53-year-old Ellis, who will step down from the team in October.
Marcelo Bielsa and the Leeds United squad were given the Fifa Fair Play Award, despite the "spygate" incident, where the Argentinian sent a scout to watch Derby County training ahead of their match.