A statement said the club “would like to express their gratitude to Ronald for the service he has given to the club over the past 16 months”.
The Toffees are 18th in the Premier League and have won just two of their nine league games this season.
“I still believe I can change the whole situation,” Koeman had said on Sunday.
Everton sack Koeman – reaction and debate
Analysis: Where has it gone wrong for Ronald Koeman?
Koeman became the third Premier League managerial casualty of the season after Frank de Boer left Crystal Palace and Craig Shakespeare was sacked by Leicester.
The 54-year-old Dutchman, who guided Everton to seventh place in his first season in charge last term, paid the price for a poor start to this season despite having spent £140m in the summer.
Everton’s majority shareholder Farhad Moshiri gave Koeman his backing a fortnight ago after their 1-0 defeat by Burnley, but the Toffees then drew at Brighton and lost to Lyon, in the Europa League, before their Goodison Park humbling by Arsenal.
Everton’s chances of progressing from Europa League Group E are slim, with the Merseysiders bottom after defeats by Atalanta and Lyon and a draw with Apollon Limassol.
On Sunday Koeman tweeted that getting a result against Arsenal was “impossible” after being reduced to 10 men while losing 2-1.
Koeman reported for training at the club’s Finch Farm base on Monday morning, with preparations for Wednesday’s Carabao Cup game at Chelsea seemingly under way.
But chairman Bill Kenwright and chief executive Robert Elstone were later reported to have arrived unexpectedly and Koeman’s dismissal was confirmed soon after.
Everton’s decision to sack Ronald Koeman completes a dramatic fall from grace for the manager who guided them back into Europe in his first season.
There was an air of inevitability that major shareholder Farhad Moshiri and chairman Bill Kenwright would be making the journey to Everton’s Finch Farm training headquarters to deliver the bad news after the debacle of the 5-2 loss to Arsenal at Goodison Park on Sunday.
Koeman had lost his way after a summer of activity in the transfer market that was extensive but failed in its main task – to replace leading goalscorer Romelu Lukaku following his £90m move to Manchester United.
He should not take sole responsibility for that, director of football Steve Walsh is also an architect of Everton’s transfer strategy, and it may be a key part of the story when Koeman delivers his version of his final days.
Koeman, however, has still overseen more than £140m worth of spending since the summer only for Everton to currently lie in the relegation zone, leaving his position unsustainable.
He has seemed unable to settle on his best team and best formation, leaving Everton – a club with no history of an appetite for short order sackings – to make the painful call on the man who was Moshiri’s first and only choice when he was lured from Southampton in summer 2016.
One of the criticisms of Koeman, a cold and calculating realist, was that he had no bond with Everton and was simply passing through on his way to better things. He may find those better things harder to find after the failures that led to his sacking only nine Premier League games into this season.
Timeline – 24 hours to a sacking
Sunday PM: Koeman on brink as Everton thrashed 5-2 by Arsenal at Goodison – watched by majority shareholder Farhad Moshiri and chairman Bill Kenwright
Monday AM: Koeman arrives at Finch Farm for training as normal
Monday Noon: Sources close to Koeman tells BBC he retains support of the club
Monday PM: Kenwright and chief executive Robert Elstone meet at Finch Farm. Moshiri signs off decision to sack Koeman
Monday 1.30PM: Everton release statement confirming Koeman sacking