Benzema, who played a pivotal role in Real's run to the Champions League title last season, is the first French player to win the trophy since Zinedine Zidane in 1998 and the fifth after Raymond Kopa, Michel Platini and Jean-Pierre Papin.
"This prize in front of me makes me really proud. When I was small, it was a childhood dream, I never gave up... Anything is possible," Benzema said on stage at the ceremony.
"There was a difficult period when I wasn't in the French team but I never gave up. I'm really proud of my journey here. It wasn't easy, it was a difficult time for my family as well."
Benzema beat Poland's Robert Lewandowski, Sadio Mane of Senegal and Belgium's Kevin De Bruyne after Argentina's Lionel Messi won the award for a record seventh time last year.
Benzema had a stellar season with Real, scoring 44 goals in 46 games in all competitions as he helped guide them to a LaLiga and Champions League double. His 15 goals in the Champions League guided Real to a record-extending 14th title.
Real made remarkable comebacks from losing positions in the last-16, quarter-finals and semi-finals against Paris St Germain, Chelsea and Manchester City respectively -- with Benzema scoring in each of the second legs.
The highlight of their European campaign was the 3-1 win in the second leg against PSG when the Spanish club were 2-0 down on aggregate, with Benzema grabbing a 17-minute hat-trick in the second half to stun the Ligue 1 side.
Putellas wins again
Spanish international Putellas won the women's Ballon d'Or for a second straight year, beating England's European Championship winner Beth Mead and Australia's Sam Kerr.
Putellas, who was also named FIFA Best Women's Player earlier this year, was top scorer in the Champions League last season with 11 goals and scored 18 in the Primera Division.
The 28-year-old missed the Euros for Spain, however, after suffering an anterior cruciate ligament injury on the eve of the tournament in England.
Real's Thibaut Courtois won the Lev Yashin award for the best goalkeeper last season, with the towering shot stopper making nine saves in the final to keep a clean sheet against Liverpool in a 1-0 victory in Paris.
However, the teams in the Champions League final lost out on the Best Club award, which went to Pep Guardiola's Manchester City who won a fourth Premier League title in five years.
Barca's 18-year-old midfielder Gavi picked up the Kopa Trophy for the best under-21 player, while Bayern Munich forward Sadio Mane won the inaugural Socrates award, with the Senegal international recognised for his humanitarian efforts.
Lewandowski did not go home empty handed either as he picked up the Gerd Muller Trophy for the best striker after scoring 50 goals in all competitions for Bayern last season.