Griezmann won both the Europa League and World Cup in 2018, the striker inspirational in the respective triumphs of Atletico Madrid and France.
He also won the best Federation Internationale de Football Association men's player earlier this year, beating competition from Ronaldo and Egypt's Mo Salah.
Modric's father was shown on the big screen during the ceremony at the imperious Grand Palais in Paris, wiping away tears.
Ronaldo missed out on a record sixth award, which would have moved him one ahead of Messi.
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Lyon's Ada Hegerberg was crowned the first ever female Ballon d'Or victor but the moment became shrouded in controversy when French DJ Martin Solveig - who was helping host the gala alongside David Ginola - asked the Norwegian to "twerk".
The Ballon d'Or was first awarded in 1956 and was partnered with soccer's world governing body Federation Internationale de Football Association under the title "The Best" from 2010 to 2015, until becoming its own entity again.
The 33-year-old was instrumental as Real clinched a third successive Champions League trophy last season.
Hegerberg has said she will not play for Norway at the Women's World Cup in France next June. Albert Stanislas Koumbobacko (Central African Republic) chose Frenchman Karim Benzema who didn't even feature at the World Cup - then Juventus' Mario Mandzukic in 5th, missing out Modric altogether! Yesterday, the Croatia global was announced as the victor of the award, to the surprise of many football fans.
Players like Wesley Sneijder, Xavi and Manuel Neuer have certainly had vald arguments in previous years and it was good to see Modric, who deserved to win for many reasons, get his hands on the award. "It's a huge step for women's football", Hegerberg said. I don't think the respect has been there.