As technical director, Cox will be responsible for overseeing all football-related matters at Everton's training facility, Finch Farm.
Cox's move to Everton was announced in June, but he stayed on at Manchester United to assist with the transition.
Cox's departure from Manchester United is seen as a significant loss for the club, given his impact on their youth development system in recent years.
Cox was instrumental in bringing 35 academy players to Manchester United's first team