Portugal captain Ronaldo, led his country to victory at Euro 2016, while France forward Griezmann was the top player at the tournament.
It is the first time that 25-year-old Griezmann has made the cut, but England captain Rooney is absent for the first time in the competition's 12-year history, after England crashed out of Euro 2016 to lowly Iceland.
That leaves Juventus goalkeeper Gianluigi Buffon and Real Madrid superstar Ronaldo as the only ever-presents for an award based on votes from professional players from 75 countries.
The eight newcomers also include France's N'Golo Kante and Dimitri Payet, Ivorian Serge Aurier, Spaniard Hector Bellerin, Italian Leonardo Bonucci, Belgian Kevin De Bruyne, Argentina's Paulo Dybala and England's Jamie Vardy.
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Barcelona lead the way with 12 players, two more than rivals Real Madrid, whose selected players include Welsh winger Gareth Bale.
Other big names overlooked are Manchester City pair Vincent Kompany and Yaya Toure, Chelsea's John Terry, Bayern Munich's Arjen Robben, Porto's Iker Casillas and Real Madrid's James Rodriguez.
The 55-player short list:
Goalkeepers (5): Claudio Bravo
(Chile/Barcelona/Manchester City), Gianluigi Buffon (Italy/Juventus), David de Gea (Spain/Manchester United), Keylor Navas (Costa Rica/Real Madrid) and Manuel Neuer (Germany/Bayern Munich).
Defenders (20): David Alaba (Austria/Bayern Munich), Jordi Alba (Spain/Barcelona), Serge Aurier (Ivory Coast/Paris St Germain), Hector Bellerin (Spain/Arsenal), Jerome Boateng (Germany/Bayern Munich), Leonardo Bonucci (Italy/Juventus), Dani Carvajal (Spain/Real Madrid), Giorgio Chiellini (Italy/Juventus), Dani Alves (Brazil/Barcelona/Juventus), David Luiz (Brazil/Paris St Germain/Chelsea), Diego Godin (Uruguay/Atletico Madrid), Mats Hummels (Germany/Borussia Dortmund/Bayern Munich), Philipp Lahm (Germany/Bayern Munich), Marcelo (Brazil/Real Madrid), Javier Mascherano (Argentina/Barcelona), Pepe (Portugal/Real Madrid), Gerard Pique (Spain/Barcelona), Sergio Ramos (Spain/Real Madrid), Thiago Silva (Brazil/Paris St Germain) and Raphael Varane (France/Real Madrid).
Strikers (15): Sergio Aguero (Argentina/Manchester City), Gareth Bale (Wales/Real Madrid), Karim Benzema (France/Real Madrid), Cristiano Ronaldo (Portugal/Real Madrid), Paulo Dybala (Argentina/Juventus), Antoine Griezmann (France/Atletico Madrid), Gonzalo Higuain (Argentina/Napoli/Juventus), Zlatan Ibrahimovic (Sweden/Paris St Germain/Manchester United), Robert Lewandowski (Poland/Bayern Munich), Lionel Messi (Argentina/Barcelona), Thomas Muller (Germany/Bayern Munich), Neymar (Brazil/Barcelona), Alexis Sanchez (Chile/Arsenal), Luis Suarez (Uruguay/Barcelona) and Jamie Vardy (England/Leicester).