Modric won the Champions League with Real Madrid for the third successive year and guided underdogs Croatia to the final of the World Cup this year.
After a shortlist of 3o players was selected by France Football magazine, a jury of global journalists voted on the players they considered first, second and third. "My dream as a kid was to play for a big club and win trophies and this is a dream", Modrić said after collecting the award.
The award, voted for by journalists and organised by French magazine France Football, has been dominated by Messi and Ronaldo since 2008. Brazil star Neymar was third a year ago but only 12th this time.
There was controversy when Hegerberg was asked by co-host Martin Solveig if she knew how to "twerk", to which she replied "No", and he later apologised for any offence caused. There's a lot of discussions to take and to bring on the table as a woman in 2018.
"It's all about how we respect women's football".
"I said, I think last time when I won The Best, I would change all my individual awards for the World Cup, unfortunately it didn't happen", Modric told reporters.
Modric described Ronaldo and Messi as "phenomenal players", adding: "To win means I did something really special on the pitch this year, that's why 2017-18 was the year for me".
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Hegerberg is a three-time Women's Champions League victor with Olympic Lyonnais and scored a tournament-record 15 times last season.
If Modric or indeed even Mbappe, Varane or even Griezmann manages to pip Ronaldo to the trophy it will be the first time since 2007 that a player from a country other than Argentina and Portugal wins the award.
"2018 is a dream year for me", the 33-year-old Modric said.
When describing his feelings on winning the award, Modric added: "It is hard to express my emotion and how I feel in words".
The winner, as has been rumoured for days, is somewhat controversially Real Madrid's Luka Modric, who is the clear victor ahead of Cristiano Ronaldo and World Cup winner Antoine Griezmann.
France won 4-2, but Modric was named the tournament MVP. Mbappe won the domestic treble with PSG, while Griezmann scored twice for Atletico Madrid in the Europa League final win against Marseille. Leo Messi was surprisingly relegated to fifth place. Modric had never previously been in the top three.