Councillor Paul Nickerson, a Conservative who sits on East Riding of Yorkshire Council, initially claimed the image had been posted onto his Twitter account by a friend with access to his account but has now accepted "full responsibility" for the message.
Mr Corbyn is donating the damages he has received to a number of different charities, including one in Liverpool.
A statement from Coun Nickerson, who has been suspended from the Conservative group on the council as a result of the tweet, said: "On November 15 2021 a defamatory tweet, for which I accept full responsibility, was published on my Twitter account.
"The tweet targeted Jeremy Corbyn and included a fake photograph of him laying a poppy wreath at the site of a burning taxi outside the Liverpool Women's Hospital where a terror attack had taken place on Remembrance Sunday killing a suicide bomber and injuring others.
"The false photograph, captioned by the word 'unsurprisingly', gave the completely untrue impression that Jeremy Corbyn supports terrorist violence including suicide bombings, which without any hesitation I wholly accept he does not.
"Without reservation I fully withdraw any suggestion or inference that Jeremy Corbyn is a supporter of terrorist violence.
"The tweet was wrong and I retract it.
"I unreservedly and sincerely apologise to Mr Corbyn for the hurt and distress that has been caused to him by the tweet.
"I entirely accept that the posting of the message the day after Remembrance Sunday aggravated the hurtful nature of the defamatory tweet.
"Accordingly, I have agreed to pay Mr Corbyn substantial damages, which he is donating to charity, and his legal costs."
Mr Corbyn said: "The bomb attack on Liverpool Women’s Hospital on Remembrance Sunday was a horrific crime, which could have killed or maimed countless victims, including new mothers and their babies.
"Councillor Paul Nickerson’s photoshopped Twitter post about me failed to understand the seriousness of the threat and did a disservice to all those affected by the attack and their loved ones.
"So I welcome his decision to apologise for his defamatory post, to agree not to repeat the tweet which he has deleted and to pay substantial damages and legal costs.
"This substantial settlement will be used to support charities that are close to my heart: including one in Liverpool and one in my constituency.”
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