The BBC and Sky Sports News HQ broke the news earlier this afternoon, with the Liverpool Echo initially more cautious after a club spokesman insisted talks were not yet complete.
However, Koeman's agent Rob Jansen has since confirmed that an agreement is in place for the Dutchman to succeed Roberto Martinez at Goodison Park.
BBC Solent say Koeman's appointment will not be confirmed until tomorrow, which perhaps explains the Echo's initial caution.
It is believed that Everton will pay in the region of £5million for Koeman and two members of his backroom staff , brother Erwin and fitness coach Jan Kluitenberg.
However, Sammy Lee and Dave Watson - who were at Southampton prior to Koeman's arrival - are likely to remain at St Mary's