The 53-year-old Koeman, who has been Southampton manager for the last two years, will take over at Goodison Park from Roberto Martinez, who was sacked just before the end of last season.
Former Ajax Amsterdam coach Koeman joined Southampton in 2014 from Feyenoord and guided the south coast club to respectable seventh and sixth placed finishes in his two seasons.
Everton finished 11th last season but are set for significant investment after Iranian businessman Farhad Moshiri purchased a 49.9 percent stake in the club.
Koeman has been widely praised for his work at Southampton where he enjoyed a 47 percent win rate in the Premier League.
Before moving into management he also enjoyed a glittering playing career, winning the European Cup with PSV Eindhoven and Barcelona in 1988 and 1992 respectively.
Former Southampton forward Matthew Le Tissier expressed his surprise at Koeman's likely move.
"He may feel he has got a better chance of winning trophies at Everton. I'd be of a slightly different opinion," Le Tissier told BBC Sport.
"I understand they've got a new owner and want to splash a bit of cash, but it might not be as easy a job as he thinks."
(Reporting by Ed Osmond; editing by Martyn Herman/Toby Davis)
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