The winger has landed in the Principality to undergo a medical ahead of his move to the eight-time top flight champions.
The Toffees were forced to sell the former Eupen man to Monaco because he was not issued a work permit to play in the Premier League for the third successive season.
An agreement has been reached on contractual terms, with the 22-year-old expected to put pen to paper on a five-year deal.
Onyekuru initially rejected joining Monaco as his priority was to return to Galatasaray where he shone last season but Everton have convinced him that the move is the right one.
He contributed to 22 goals (16 goals, 6 assists) in 44 games over the course of last season, helping Galatasaray with the Super Lig and Cup.