Essendon's board met on Sunday and decided to cut ties with Rutten, who was contracted for next season but had been on shaky ground in recent weeks.
The Bombers this week announced plans for an external review and openly and unsuccessfully chased Clarkson as Rutten's replacement.
Rutten departs after coaching the Bombers to 17 wins and 26 losses across two seasons, including leading them to finals in his first campaign in 2021.
Essendon will now search for their third coach in four seasons and have already been linked to a potential reunion with former mentor James Hird.
"Ben's commitment and care for this playing group was second to none, and we thank him for his dedication to what we recognise is an all-consuming role as senior coach," president David Barham said in a statement.
"The unfortunate reality is, at various stages this season; we have simply been uncompetitive. And while we acknowledge that we have an emerging playing list, we were compelled to make the decision.
"Our members and supporters do, and should, expect better from a proud football club.
"We appreciate this has been a difficult chapter for our club. But as I said in my president's address pre-game yesterday, we will be a bold and courageous football club again.
"We need to return to being a successful football club.
"We will thoroughly and diligently consider our next steps and in due course, will communicate the process of our next senior coach appointment."
Rutten replaced John Worsfold as part of a handover after the 2019 season.
He was emotional in the rooms after Saturday night's 66-point loss - 21.15 (141) to 11.9 (75) - to Richmond but said he wanted to stay on despite "disappointing" treatment from the Bombers.
New president Barham apologised on Friday for failing to notify Rutten of Essendon's late pursuit of Clarkson.
"It's been disappointing. I probably think I deserve better," Rutten said.
"As a club, we need to come together as a whole football club and we need to stick to a plan, put our heads down, bum up and do the work.
"There's no other way for this football club to get back to where it wants to be."
The Bombers had come under criticism for their late attempt to lure Clarkson, including scathing assessment from former captain Jobe Watson.
"At least they're consistent. They consistently don't know what they're doing and they consistently get it wrong," Watson told the Seven Network.
"For me, it's a reflection on the culture of the club and they are operating in silos, there is no cohesion between football departments, upstairs, board.
"They are all looking outward instead of looking inward. They are a dysfunctional place."
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