Compatriot Andre 'Dede' Ayew, Ivorians Didier Drogba and Yaya Toure and Cameroonian Samuel Eto'o were the other finalists with listeners voting online and by text.
"It was really hard to win this award especially because of all the other players I was up against," the striker who joined Sunderland from Rennes in a $20 million mid-year dea,l told the Fast Track radio show.
Gyan scored three of the four goals that took Ghana to the African Nations Cup final last January, and grabbed another three in South Africa, as the Black Stars became only the third African country to make the last eight in the world cup.
And the west Africans could have gone even further had Gyan converted a penalty in the dying seconds of stoppage time against Uruguay, instead of blasting the ball against the crossbar.
Gyan is also a contender for the CAF African Footballer of the Year award, with Eto'o and 2009 winner Drogba, and the result of a poll among national coaches will be announced on Monday in Cairo.