The right-wing conspiracy theory website agreed the payout after using the cartoon frog on a poster.Read more
Twitter says it has permanently suspended the accounts of Alex Jones and his Infowars website.
It made the move after a number of tweets that violated Twitter's abusive behaviour policy, the company said.
A number of tech giants, including YouTube and Facebook, deleted the right-wing conspiracy theorist's content last month, citing hate speech.
The radio host is currently being sued for defamation by the parents of two children killed in the 2012 Sandy Hook Elementary School shooting, which he has repeatedly claimed was a "giant hoax". Twenty children under the age of seven and six adults died in the attack.