Ms Riley, 36, who appears on the Channel 4 show Countdown, won a claim against Laura Murray, who is in her early 30s and used to work for the former Labour leader, in December last year.
Mr Justice Nicklin rejected Ms Murray’s defences of truth, honest opinion, and publication on matter of public interest and awarded damages to Ms Riley, saying she was entitled to “vindication”.
Ms Murray challenged that ruling at the Court of Appeal in July, but her appeal was dismissed by three senior judges in a ruling delivered on Thursday.
During the trial last year, Mr Justice Nicklin heard both women posted tweets after Mr Corbyn, who was then Labour leader, was hit with an egg while visiting a mosque in March 2019.
Ms Riley posted a screenshot of a January 2019 tweet by Guardian columnist Owen Jones about an attack on former British National Party leader Nick Griffin, which said: “I think sound life advice is, if you don’t want eggs thrown at you, don’t be a Nazi.”
She added “Good advice”, with emojis of a red rose and an egg.
Later, Ms Murray tweeted: “Today Jeremy Corbyn went to his local mosque for Visit My Mosque Day, and was attacked by a Brexiteer.
“Rachel Riley tweets that Corbyn deserves to be violently attacked because he is a Nazi. This woman is as dangerous as she is stupid. Nobody should engage with her. Ever.”
Ms Riley said she was being sarcastic in her tweet, did not call Mr Corbyn a Nazi, and told the judge that Ms Murray’s tweet caused serious harm to her reputation.
Mr Justice Nicklin concluded that the tweet meant Ms Riley had “publicly stated” Mr Corbyn had been attacked when visiting a mosque; that he “deserved to be violently attacked”; by doing so she had shown herself to be a “dangerous and stupid person” who “risked inciting unlawful violence”; and that people should not “engage with her”.
He found that Ms Riley had demonstrated that Ms Murray’s tweet had caused serious harm to her reputation, and also said both women had been truthful in the evidence they gave and had done their best to “assist the court”.
Mr Justice Nicklin said there was an “element of provocation” in Ms Riley’s “good advice” tweet.
“Although posting the good advice tweet could not be described as ‘bad conduct’ of the claimant, it properly falls to be characterised as provocative, even mischievous,” he said in a written ruling.
“It was calculated to provoke a reaction and it did.”
Ms Riley, who studied mathematics at Oxford University and is on maternity leave from Countdown after giving birth in November, had told the judge she is Jewish and has a “hatred of antisemitism”.
She said she speaks out against antisemitism and thought the Corbyn-led Labour Party was “fostering antisemitism”.
Ms Murray was stakeholder manager in Mr Corbyn’s office when he was Labour leader, and went on to be the party’s head of complaints, before going into teaching.
She argued that what she tweeted was true and reflected her honestly held opinions.
Mr Justice Nicklin ruled at an earlier hearing that Ms Murray’s tweet was defamatory.
Ms Murray told the judge that her job had involved her working with the Jewish community to “try to find solutions to the problem of antisemitism which was becoming evident within parts of the Labour Party membership”.
Lawyers for Ms Murray argued that Mr Justice Nicklin was wrong to reject her defences, saying that the “ambiguity” of Ms Riley’s initial tweet meant that Ms Murray’s subsequent tweet was “substantially true”.
They also raised objections to his rejection of the honest opinion and public interest defences.
But, giving the lead ruling, Lord Justice Warby said Mr Justice Nicklin was “entitled to conclude that … the defendant’s tweet was not shown to be substantially true”.
The judge, sitting with Lords Justice Dingemans and Arnold, also rejected Ms Murray’s other grounds of appeal.