Poland striker Lewandowksi struck 15 times in 10 games as Bayern won the Champions League last season, while also contributing 34 league goals as the Bavarian side added the Bundesliga title.
Lewandowski overcame fellow finalists Cristiano Ronaldo and Lionel Messi to claim the award, becoming just the second player outside of the famed duo to win the award – or its previous incarnations – since 2008.
“To win such an award and share this title with Messi and Ronaldo, is unbelievable and means so much to me,” Lewandowski said.
“I am very proud and happy. This is a great day for me, and also for my club and colleagues.
“This award also belongs to my colleagues, the coach and Bayern in general. It is an incredible feeling, a lot of emotions.”
Lewandowski’s agent Pini Zahavi hit out at world football’s governing body, while congratulating his player on the award.
He told Sky in Germany: “FIFA and the world of football have finally recognised Robert as the best player in the world this year. If Robert had been born in another country, I am sure he would have received this trophy a long time ago already.
“I want to congratulate him, his family and all of his millions of supporters. He is not only the best scorer in the world, but an example of a great athlete and personality. Bayern Munich and myself – we are very proud to have him.”