The club will compensate the manager with about £5m as he leaves Premier League rivals Southampton after two years in charge.
Former coach Roberto Martinez was sacked by the club as a result of stringent runs of awful performances in the league at the just concluded season.
A deal with the Dutchman, headhunted by new owner Farhad Moshiri, was agreed earlier in the week and is reported to be worth about £6m a year.
Koeman led the Saints to a seventh and sixth position respectively in his two year reign at Southampton.
The new manager is expected to be joined at Goodison Park by brother Erwin and fitness coach Jan Kluitenberg.