Jack Monroe, a food blogger who also campaigns over poverty issues, sued Hopkins over two “war memorial” tweets, asking a judge in London to find she was “defamed” by the former Apprentice contestant.
Following a recent hearing, Mr Justice Warby ruled in Monroe’s favour on Friday.
Monroe tweeted: “It”s taken 21 months but today the High Court ruled that Hopkins statements to/about me were defamatory. I sued her for libel. and I won.”
The case arose after Twitter erupted following the daubing of a memorial to the women of the Second World War in Whitehall with the words “F... Tory scum” during an anti-austerity demonstration.
Monroe took legal action over what her lawyer told the judge was a “widely published allegation” that she had “either vandalised a war memorial or approved of such an act”, an allegation that would “inevitably cause serious damage to reputation”.
Jonathan Price, for Hopkins, told the judge her case was “this relatively trivial dispute arose and was resolved on Twitter in a period of several hours”.
He argued “no lasting harm, and certainly no serious harm”, to Monroe’s reputation resulted from it.
Hopkins had “mistakenly” used Monroe’s Twitter handle instead of that of another columnist who had tweeted about the war memorial incident.
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But Mr Justice Warby ruled “whilst the claimant may not have proved that her reputation suffered gravely, I am satisfied that she has established that the publications complained of caused serious harm to her reputation”.
He said their publication “not only caused Ms Monroe real and substantial distress, but also harm to her reputation which was serious”.
The judge concluded: “Ms Monroe is entitled to fair and reasonable compensation, which I assess at £24,000.”
Speaking after the decision was announced, Monroe said: “I am very relieved that it is over and done with.
“It has been a very long and very arduous process. There have been many times when I have almost given up and walked away. But I started something and I had to see it through, and I have done.”
Monroe’s lawyer, Mark Lewis, a partner at Seddons solicitors, said she had “finally been vindicated in full from the libellous and wholly false accusation by Katie Hopkins that she had supported the vandalisation of a war memorial”.
He added: “Jack Monroe never did, and coming from a proud military family, never would.
“Despite pointing this out to Katie Hopkins within minutes of her first tweet wrongly accusing Jack, Hopkins did not apologise.
“Rather the self-styled ‘rent-a-gob’ defiantly posted another defamatory tweet. The price of not saying sorry has been very high.
“Despite repeated opportunities to back down, Hopkins obstinately refused to apologise, instead conducting her defence by slinging as much mud as she could to hide the fact that she had made this false allegation.”
He added: “The price of not saying sorry has been very high. Hopkins has had to pay out of her own pocket a six-figure sum in damages and costs for a tweet that should have been deleted within minutes as soon as she was told it was wrong. On this occasion, the cost of renting that gob was particularly high.
“Hopkins claimed that Twitter was just the wild west where anything goes. The judge has shown that there is no such thing as a Twitter outlaw.”
After announcing his decision, Mr Justice Warby ordered Hopkins to pay £107,000 on account of costs within 28 days - the final costs figure has yet to be assessed.
At the heart of the action was a posting on Twitter in May 2015.
Hopkins wrote: “@MsJackMonroe scrawled on any memorials recently? Vandalised the memory of those who fought for your freedom. Grandma got any more medals?”
The judge ruled that the tweet “meant that Ms Monroe condoned and approved of scrawling on war memorials, vandalising monuments commemorating those who fought for her freedom”.
He found that a second tweet “meant that Ms Monroe condoned and approved of the fact that in the course of an anti-government protest there had been vandalisation by obscene graffiti of the women’s war memorial in Whitehall, a monument to those who fought for her freedom”
The judge added: “These are meanings with a defamatory tendency, which were published to thousands.”
Mr Justice Warby - who attached an appendix to his judgment entitled “How Twitter Works” - said: “This case has been about the particular tweets complained of by this claimant against this defendant. It may have little wider significance.”
The judge said Hopkins’s answer to the claim was that her tweets did not bear the meanings complained of, were not defamatory and that it had not been shown that they caused serious harm to Ms Monroe’s reputation.
She did not give evidence during the trial.
Mr Justice Warby said that for the purposes of the case, Hopkins described herself as “confrontational, outspoken, forthright, often outrageous and frequently flippant in her journalism and social media activity, and very well known as such”.
Media lawyer Mark Stephens, of law firm Howard Kennedy, said: “People need to understand that being rude or defamatory on social media is permanent and indelible, and you can be sued.
“The courts will allow robust debate and will consider posts and comments to see if they were meant as fact or a joke. But the fact remains that if comments cause serious harm, legal action is likely to follow.”
He added: “This is a particularly expensive mistake by Katie Hopkins as Jack Monroe offered to settle for the traditional sum of £5,000 on the day of the Twibel.
“But Mr Justice Warby has now set a tariff at £24,000 for Twibel cases. This is a level which will undoubtedly encourage more claims. People now need to be careful with their tweets - don’t tweet now and repent at leisure.”
Emma Woollcott, a lawyer at Mishcon de Reya who specialises in reputation protection, said: “This sensible decision demonstrates how serious harm and distress can be caused by defamatory tweets, and how significant costs might have been avoided by Hopkins - when she realised her apparent mistake - by proper contrition and a prompt apology.”
Last year, an article by Hopkins resulted in a £150,000 libel damages payout for her publisher. In a column for MailOnline in 2015 the TV and radio personality wrongly suggested two brothers were extremists with links to al Qaida.