With five Ballon d'Ors each, their domination began in 2008 with the Portuguese attacker winning as a Manchester United player.
He then followed that up by captaining Croatia to the World Cup final for the first time in their history - deservedly winning the Golden Ball for the tournament thanks to his incredible displays in the middle of the park.
Messi finished fifth in the voting, with Griezmann's France team-mate Mbappe a place above the Barcelona star. The other main contenders won just one or the other, or neither.
The top ten included: Harry Kane (ENG/ Tottenham Hotspur), Kevin De Bruyne (BEL/ Manchester City), Eden Hazard (BEL/ Chelsea), Raphael Varane (FRA/Real Madrid), Mohamed Salah (EGY/Liverpool), Lionel Messi (ARG/Barcelona), Kylian Mbappe (FRA/Paris Saint-Germain), Antoine Griezmann (FRA/Atletico Madrid), Cristiano Ronaldo (POR/Real Madrid), Luka Modric (CRO/Real Madrid). "I have sensational feelings in me at the moment which I find hard to describe".More news: HIV Diagnosis At Its Peak In Eastern Europe
It was his performances in the tournament in Russian Federation which began to swing the balance, as he won a variety of individual awards including UEFA's Best Player in Europe and FIFA's The Best in October, as well as the Golden Ball for the best player last summer in Russian Federation.
France worldwide and Paris Saint-Germain striker Kylian Mbappe has won the inaugural Kopa Trophy for the best Under-21 player. The 19-year-old became the second-youngest to ever score in a World Cup final as he helped France to their second title this summer.
If Modric does indeed lift the trophy, it will be the first time since 2007 - when Kaka won the award - that it has not gone to Messi or Ronaldo.
Real Madrid's Thibaut Courtois, formerly of Chelsea, was the highest-ranked goalkeeper in this year's Ballon d'Or list in 14th, while his former Blues teammate N'Golo Kanté took 11th place.