Lookman scored a hat-trick as his Italian club Atalanta won the Europa League final against Bayer Leverkusen in Dublin in May and earlier in the year helped Nigeria reach the Africa Cup of Nations final in the Ivory Coast.
He netted three times at the AFCON tournament.
"This award is a blessing, to be recognised as best player in Africa is something incredible," he said.
"Four years ago my career fell down but now I'm here as the best player in Africa. Don't let your failures stop your dreams."
Lookman was named ahead of Morocco's Achraf Hakimi, Serhou Guirassy of Guinea, Simon Adingra from the Ivory Coast and South Africa goalkeeper Ronwen Williams.
The award is voted for by a panel that includes national team coaches and captains, but no details of the voting tallies were immediately provided.
Lookman is the seventh Nigerian to take the award and succeeds last year’s winner Victor Osimhen.
Nwankwo Kanu (twice), Emmanuel Amunike, Victor Ikpeba and Rashidi Yekini are the other previous Nigerian winners.
Zambia's Barbra Banda was named African Women’s Player of the Year.
Two years ago she was left out of the squad for the Women’s Africa Cup of Nations finals on gender eligibility grounds but was cleared by FIFA to compete at the 2023 Women’s World Cup and played at this year's Paris Olympics.