The award, voted for by journalists and organised by French magazine France Football, has been dominated by Barcelona's Messi and Ronaldo, first when he was at Manchester United and subsequently with Real Madrid, since 2008.
Griezmann won both the Europa League and World Cup in 2018, the striker inspirational in the respective triumphs of Atletico Madrid and France.
Modric, 33, was also named FIFA's Best Men's Player earlier this year.
Among the 30 players who were shortlisted for the Ballon d'Or, only two players did not get a single point by the end of the voting - Real Madrid and Spain's Isco and Tottenham Hotspur and France's Hugo Lloris. I want to thank my teammates and coaches at Real Madrid and those with the national team.
Olympique Lyonnais' Norway forward Ada Hegerberg won the inaugural Ballon d'Or for women's football, having led her side to the Women's Champions League title, scoring in extra time in the 4-1 win over Vfl Wolfsburg in the final. Stats-wise, the midfielder was nowhere near Messi and Ronaldo, but his performance in the World Cup seems to have swayed the votes in his favour. "So even if I don't win, we win", Kerr posted on Instagram before the awards ceremony overnight.
The reaction, save for the Ronaldo and Messi loyalists, has been largely positive to the newly-crowned best player in the world.
Luka Modrić wins the 2018 Ballon d'Or
"I've two years left on my [Madrid] contract, and hopefully some more than that", Modric said.
Modric's Ballon d'Or victory is the 11th such occasion for Real Madrid.
With the result widely known even before the ceremony, World Cup 2018 victor Griezmann said on his way into the building: "It's a pity that a Frenchman didn't win. I am very happy". Hegerberg is a three-time Women's Champions League victor with the French side and scored a tournament-record 15 times last season.
Monday was a big day for many people in the football galaxy.