Monaco announced that the Nigerian international signed a five-year contract.
Although neither side revealed a fee, Joe Bernstein of the Daily Mail reports that Everton agreed to sell the 22-year-old for £12 million.
"We are very happy to have Henry Onyekuru with us," Monaco general manager Oleg Petrov said. "He has demonstrated his qualities in recent seasons. He is a fast and powerful offensive player who will strengthen our offensive sector. We welcome him."
He scored 16 times in 44 appearances to help the Turkish side win the Super Lig.