He announced his departure at a media conference at Windy Hill, saying his job had been to steer the club through a period of crisis to a point of stability.
Robson, who has been under pressure since the announcement of the Australian Sports Anti-Doping Authority's inquiry into the Bombers' controversial supplements program last season, said he first offered his resignation in February, but this had not been accepted.
He said now was the time for the club's board to look for a new CEO, and that resigning was the right and honourable thing to do.
"Accountability rests with me, and I accept that."
Earlier this month, the Ziggy Switkowski report into the club's management processes didn't call for anyone to be sacked, but highlighted a lack of managerial responsibility.
"The CEO must be accountable for everything that happens within his organisations," it said.
"Coaches cannot bypass him, and boards must work through him."
Robson accepted that a CEO was at the "front line of accountability" and should know what was happening throughout a business.
"Ziggy put down a very clear and fundamental challenge; he acknowledged that I didn't know but he also made clear that CEOs should be across everything and for that, today, I'm accepting accountability and it's for that reason I've made known my resignation to the board today and it's been accepted.
"We now know that a lot happened at this club in 2012 that just should not have happened.
"We let down our players and their families; how seriously we let them down is still a matter of investigation … there is no excuse in not knowing.
"A lot of criticism has been levelled at the [Australian Crime Commisision], ASADA and the 'blackest day in sport' press conference.
"I want to make it clear that we must use these events as a turning point in sport. If you care about sport then respect the people that are trying to investigate what happened. If there is a line in the sand, I want to be on the side that puts first the health and safety of the players and the underlying fairness of the game."
Robson said he had "learnt a lot over the last few months, and I hope my commitment to the club and to doing the right thing during this period will serve to make some amends for the serious failings of last year.
"I am now going to commit myself to becoming a better sports administrator."
Essendon chairman David Evans said he had "nothing but the highest praise" for Robson's role in stabilising the club, but a chief executive must take responsibility for what happened on his watch.
"As Ian has made clear, any good CEO must be accountable for the failures that have happened in their organisation, and there's no doubt the club made mistakes in 2012.
"On the back of Ziggy's report, Ian has put his hand up today to accept accountability for what has happened on his watch, but [I] also hope that in time he does get the recognition for the great things he's done for our club."
Evans said the club felt it had now reached a level of stability that enabled it to accept Robson's resignation, which was offered again on Thursday morning.
An interim CEO would be announced in the next 24-48 hours after the Essendon board met on Thursday afternoon for more than four hours.
Speculation on Thursday suggested recently departed Melbourne Storm chief executive Ron Gauci could be a candidate to become the Bombers' boss.
But contacted by AFL.com.au, Gauci said he had not been contacted by Essendon.
Asked if he'd be interested in the vacant position Gauci responded: "That's a hypothetical."
Evans said ASADA's interviews with players had almost finished, and while he could not say when it would conclude "we are at least beginning to sight the end" of the inquiry process.
In February, after revelations of the ASADA inquiry came to light, Robson stood down from the working party of AFL club officials that came together to tackle the competition's issue with illicit drugs.
On Wednesday Robson appeared before the media to explain what happened to Nathan Lovett-Murray after the player was stabbed in a domestic dispute.
Robson is in his fourth season at Essendon after holding the same position at Hawthorn for five years.
He played a major part in the Hawks' 2008 premiership after reinvigorating the club with its Waverley Park base.
Late last year, Robson was linked to the then-vacant role of NRL CEO as his three-year contract at Essendon cameto an end.
He remained at Windy Hill, and while the Bombers didn't say how long his contract extension was, the club stressed he was the man to lead it into its next phase at its new Melbourne Airport base.
Before his stint with Hawthorn, Robson held various roles in Australia and overseas, including as the head of SportScotland, the national strategic body for sport in Scotland.
