In a column for MailOnline in 2015 the TV and radio personality wrongly suggested two brothers were extremists with links to al Qaida.
Hopkins and MailOnline have also apologised for the column entitled “Just because Britain’s border security is a Mickey Mouse operation you can’t blame America for not letting this lot travel to Disneyland - I wouldn’t either”.
In the article, Hopkins said she did not believe Tariq Mahmood and his brother Zahid Mahmood were really flying to America with their children to visit Disneyland and said Homeland Security were right to refuse them entry to the country.
An apology published on MailOnline for the December 23 2015 article said: “We are happy to make clear that Tariq Mahmood and Zahid Mahmood are not extremists, nor do they have links to al Qaida.
“They were travelling to the USA with their families to see one of their brothers for a holiday in California and they had indeed planned to visit Disneyland as part of their trip.”
The website also apologised for a second column by Hopkins, published on December 29 2015, that suggested that Tariq Mahmood’s son, Hamza, was responsible for a Facebook page which allegedly contained extremist material.
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As well as the libel damages the family’s legal costs will also be met by the publisher.
The apology - which was tweeted by Hopkins in the early hours of Monday - added: “Hamza Mahmood has pointed out that he is not responsible for the Facebook page, which was linked to him as a result of an error involving his email address.
“We are happy to make clear that there is no suggestion that either Hamza nor Taeeba or Hafsa Mahmood (Hamza’s mother and sister) have any links to extremism.
“We and Katie Hopkins apologise to the Mahmood family for the distress and embarrassment caused and have agreed to pay them substantial damages and their legal costs.”
In a statement on behalf of the family, Tariq and Zahid Mahmood said: “Even to this day the US authorities have not explained the reason why we were not permitted to travel; we assume it was an error or even a case of mistaken identity.
“However, matters are not helped when such sensationalist and, frankly, Islamophobic articles such as this are published, and which caused us all a great deal of distress and anxiety.
“We are very pleased that the record has been set straight.”