Robinson - whose real name is Stephen Yaxley-Lennon - was sued by Jamal Hijazi, 18, who was assaulted in the playground at Almondbury Community School in Huddersfield in October 2018.
Shortly after the video of the boy being beaten up went viral, Robinson claimed in two Facebook videos that Mr Hijazi was "not innocent and he violently attacks young English girls in his school".
In the clips viewed by nearly a million people, 38-year-old Robinson also claimed Mr Hijazi "beat a girl black and blue" and "threatened to stab" another boy at his school.
These allegations by the EDL former leader were rejected as false by Mr Justice Nicklin in a judgment on Thursday.
The judge ruled in Mr Hijazi's favour and granted him £100,000 in damages, as well as ordering Robinson to pay costs which are understood to be more than £500,000.
Robinson, who attended the remote hearing by video link, said he was "gobsmacked" by the costs Mr Hijazi's lawyers were claiming, which he said included £70,000 for taking witness statements.
He said: "I've not got any money. I'm bankrupt. I've struggled hugely with my own issues these last 12 months... I ain't got it."
At a four-day trial in April, Mr Hijazi's lawyers said Robinson's comments had "a devastating effect" on the schoolboy and his family who had come to the UK as refugees from Homs, Syria.
Robinson, who represented himself, argued his comments were substantially true, claiming to have "uncovered dozens of accounts of aggressive, abusive and deceitful behaviour" by Mr Hijazi.
However, Mr Justice Nicklin said: "The defendant took on the burden of proving his allegations to be true. He has failed.
"In reality, and for the reasons I have explained, his evidence fell woefully short. He has, however, persisted with the serious allegations he originally made, and has even added to them during the proceedings.
"The claimant has had to face them in the full glare and publicity of a High Court trial.
"It is my responsibility to make clear that the defendant has failed in his defence of truth, to vindicate the claimant and to award him a sum in damages that represents fair compensation."
The judge said Robinson's videos were "calculated to inflame the situation" and said Mr Hijazi predictably became the target of abuse and had to leave his home and abandon his education.
Mr Justice Nicklin ordered Robinson to pay Mr Hijazi's legal costs, which were not stated in court.
The judge also granted Mr Hijazi an injunction against Robinson, preventing him from repeating the allegations made against him.
Francesca Flood, from Burlingtons Legal, said: "It took great courage for our client, Jamal Hijazi, to pursue his libel action against such a prominent far-right and anti-Islam activist as Stephen Yaxley-Lennon, better known as Tommy Robinson.
"Jamal and his family now wish to put this matter behind them in order that they can get on with their lives.
"They do however wish to extend their gratitude to the great British public for their support and generosity, without which this legal action would not have been possible."