Ronaldo scored 17 goals in all as Real won the title for the 10th time. The Portuguese was presented with the award in Monte Carlo by UEFA President Michel Platini at the end of the draw for this season's Champions League.
He won ahead of Bayern Munich's Arjen Robben and Manuel Neuer in a live vote by a panel of 54 journalists.
"I'm really happy, so I must say thanks to my team-mates because without the team, individual awards would not be possible. I don't have this trophy in my museum, so my brother is going to put it there immediately," he said.
Nadine Kessler won the women's award after captaining VfL Wolfsburg to the women's Champions League title, ahead of team-mates Nilla Fischer and Martina Mueller.
Ronaldo opened a museum on Madeira in 2013 to showcase his trophies and medals.
(Reporting by Mike Collett; Editing by Robert Woodward)
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