The Toffees triggered the £6.8m release clause in his contract and he is believed to have completed a medical at their training ground on Monday evening.
He also revealed that the Nigerian striker was not able to earn a United Kingdom work permit and will now be loaned to Belgian club Anderlecht for next season.
The 20-year-old attracted interest from the Premier League, Bundesliga and Ligue 1 after finishing joint-top goalscorer in the Belgian Pro League with Eupen.
Everton feel another season spent with Anderlecht, who will be playing in the Champions League, will be significant for Onyekuru's development and he will arrive at Goodison Park in 12 months' time a much more polished forward.
Born in Onitsha, Nigeria on June 5, 1997, Onyekuru joined Aspire Academy in Senegal in 2010.
The Malaga striker is now on global duty with Spain at the European under-21 Championships in Poland which has held up his Blues unveiling.
He is Everton's third signing of the summer following their record-breaking signing of £30million goalkeeper Jordan Pickford from Sunderland.
Everton are also interested in Swansea midfielder Gylfi Sigurdsson and Burnley centre-back Michael Keane.