Or provide evidence that he is a racist.
Mr Hijazi was filmed being attacked in the playground at Almondbury School in Huddersfield in October 2018.
Shortly after the video of the assault went viral, Mr Yaxley-Lennon claimed in two Facebook videos that the teenager was "not innocent and he violently attacks young English girls in his school".
In clips viewed by nearly one million people, the 38-year-old also claimed Mr Hijazi "beat a girl black and blue" and threatened to stab another boy at his school, allegations denied by Mr Hijazi.
"As was entirely predictable, the claimant then became the target of abuse which ultimately led to him and his family having to leave their home, and the claimant to have to abandon his education.
"The defendant is responsible for this harm, some of the scars of which, particularly the impact on the claimant's education, are likely to last for many years, if not a lifetime."
The judge said Mr Yaxley-Lennon's defence that the "very serious" allegations were substantially true had not been proved, and he had used language "calculated to inflame the situation".
"The defendant's contribution to this media frenzy was a deliberate effort to portray the claimant as being, far from an innocent victim, but in fact a violent aggressor," he added.
At a further hearing, the judge granted an injunction against Mr Yaxley-Lennon preventing him from repeating the allegations.
The final damages and costs figures will be agreed and submitted to the High Court at forthcoming hearings to establish Mr Yaxley-Lennon's means and assets.
The High Court orders the anti-Islam activist to pay a teenage refugee £100,000 in damages.
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