Paul Nickerson, a councillor for East Riding, apologised for the image, which showed Corbyn laying a wreath at the scene of the attack outside Liverpool Women's Hospital.
A bomb was detonated inside a taxi on Remembrance Sunday, killing a man and injuring another.
Mr Nickerson said the post gave the “completely untrue impression” that Mr Corbyn supports terrorist violence and said the tweet was “wrong”.
In a statement on Twitter, the councillor said: "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."
Commenting on the settlement of the legal case, Jeremy 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."
In a statement last week, Jonathan Owen, leader of the Conservative group on East Riding Council, said "inappropriate remarks" would not be tolerated.
Mr Owen said: "Following an inappropriate and offensive message, which appeared on councillor Paul Nickerson's Twitter feed, I have suspended him from the East Riding of Yorkshire Council Conservative group with immediate effect and an investigation will now take place."