The 20-year-old forward is the first player to win the new award from the BBC World Service, voted for by football fans around the world.
She beat Spain’s Veronica Boquete, German Nadine Kessler, Scot Kim Little and Brazilian Marta to the honour.
“I would like to say thank you to the BBC, to my fans around the world and to everyone who voted,” she said.
The award is the first of its kind hosted by a global broadcaster.
Oshoala, who was the youngest player to be shortlisted, was the leading scorer at the Under-20s World Cup in Canada last summer and was voted the tournament’s best player.
Her performances led Nigeria to the final, where they were narrowly beaten by Germany, and she was also a major influence in the senior Nigeria team who won the African Women’s Championship in October.
That ensured their qualification for this summer’s World Cup in Canada, which begins on 6 June with full coverage on the BBC.
Oshoala said the honour was a big lift for Nigeria before the World Cup and would help inspire young players in her homeland.
“It’s a really good thing for us as a team because we now know that we have something great and now we want to go at the trophy,” she said. “We can do it, we did it in 2014 we can also do it this year as well.
“There is going to be a lot of motivation for women’s football in Nigeria now because of this award because there are a lot of fans out there.
“Support for women’s football in Nigeria is now growing very high.
“I know my Liverpool Ladies coach is going to be happy right now. Before I left the UK he called me and said to me ‘don’t worry I hope you win the award and we’re going to celebrate it when you come back’.”
Oshoala signed for Liverpool Ladies in January 2015, becoming the first African to feature in the Women’s Super League, with manager Matt Beard calling her “one of the world’s top young footballers”.
Mary Hockaday, controller of BBC World Service English, paid tribute to Oshoala.
“At still only 20, she’s proved herself a formidable talent on the pitch,” she said. “I’m proud BBC World Service is supporting the women’s game and thrilled with the interest in the award.”