Bayern Munich striker Lewandowski saw off competition from Lionel Messi and Cristiano Ronaldo to be crowned the best men's player.
The forward has been in frightening form over the last year, scoring 55 goals and firing Bayern Munich to an impressive treble last season.
He was widely tipped to win the Ballon d'Or this year before it was scrapped amid the pandemic.
Lewandowski has continued his form and, since the start of the 2019/20 season, he has scored 73 goals in 64 club games -- 22 more than any other men's player in Europe's top five leagues.
"This award also belongs to my colleagues, the coach and Bayern Munich in general. It is an incredible feeling, a lot of emotions," he said.
"If you win such an award and share that title with Messi and Ronaldo, that is unbelievable and it means so much to me. A long time ago, I remember I was longing for something like this and now I can win such an award."
'I will remember this moment'
Manchester City's Bronze was named the best women's player of the year, becoming the first defender to do so.
Bronze won the league title, domestic cup and Champions League with Lyon last year before moving back to England at the start of the new season.
The England international beat Chelsea's Pernille Harder and Lyon's Wendie Renard to the prize.
"What a surprise. To even be nominated alongside the two other players, they are both incredible players and outstanding human beings well," Bronze said over video call.
"I don't think I have the words right now to explain how I am feeling. If there is anything 2020 has taught us it is to appreciate every moment you have, never look too far ahead and live in the hear and now," she said. "I will appreciate winning this award now more than ever, and I will remember this moment for the rest of my life."
The awards recognize achievements made between July 20, 2019, and October 7, 2020. The voting is split between team captains, national team coaches, fans and 200 journalists.
Meanwhile, Jurgen Klopp was named the best men's coach of the year after guiding Liverpool to its first league title for 30 years last season -- with a club-record total of 99 points.
He beat Bayern Munich boss Hans-Dieter Flick and Leeds United manager Marcelo Bielsa to the prize.
Many had expected Flick to take the title after guiding Bayern to victory in the Bundesliga, Champions League, German Cup, German Super Cup and UEFA Super Cup last year.
Netherlands manager Sarina Wiegman won the award for best women's coach after transforming the national team's fortunes since the 2019 World Cup -- overseeing a 10 game unbeaten streak.
Elsewhere, Bayern's Manuel Neuer was crowned best men's goalkeeper while Lyon's Sarah Bouhaddi took home the best women's goalkeeper award.