Hegerberg was one of seven players from the all-conquering Lyon side to feature among the 15 nominees, but she won out thanks to her prolific form in front of goal.
"I would like to end this speech with some words to young girls all over the world: Please believe in yourself".
"I explained to [Ada Hegerberg] the buzz and she told me she understood it was a joke".
Hegerberg is a three-time Women's Champions League victor with French side Lyon and scored a tournament-record 15 times last season.
Solveig then tweeted a photo from backstage in which he is shaking hands with Hegerberg.
Picking up the maiden award, Solveig proceeded to ask Hegeberg whether or not she could, nay would, "twerk". I didn't know this would be seen as such an offense... However, she also expressed frustration about living "in such a man's world" and said the award will not make her reconsider her refusal to play for Norway because of her unhappiness over perceived inequality.
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The 33-year-old has already lost two major awards to his former teammate Luka Modric earlier this year. Ronaldo is reported to be runner-up with World Cup victor Antoine Griezmann third in the voting.
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"Sincere apologies to the one I may have offended".
What was a huge step was taken back a notch and unfortunately Hegerberg, as with everyone watching, is reminded that no matter how high up a woman goes or what new ceiling is broken there will always farther to go.
She added seven assists across the two competitions.
Matildas star Sam Kerr finished in fifth spot in the voting, but said just having the award meant women's football had won. People who have followed me for 20 years know how respectful I am especially with women.
The Norwegian was invited onto the stage and held the trophy aloft on an evening that also saw Luka Modric become the first player other than Cristiano Ronaldo and Lionel Messi to win since 2007.
Modric was named the best player of the 2018 FIFA World Cup, and was a key member of the Real Madrid team that won a third consecutive UEFA Champions League.