The article was published on the online news website Ethiopian Review.
Judge Richard Parkes QC said it was difficult to imagine more serious allegations.
The site's publisher and editor-in-chief, Elias Kifle, had denied liability.
The judge said that instead of apologising Mr Kifle had repeated the libel and abused Mr al-Amoudi and his lawyers.
The High Court in London heard Mr Kifle's response to the initial complaint was: "Here is my formal statement: Screw yourself".
The court heard Mr Kifle then went on to describe Mr al-Amoudi as a "scumbag bloodsucker" who was "funding al-Qaeda".
Mr al-Amoudi, 65, gave evidence during the libel trial that he was completely opposed to all forms of terrorism.
The judge said the site alleged that Mr al-Amoudi had "disgracefully and callously" married off his daughter Sarah, then 13, to an elderly member of the Saudi royal family as a gift.
'Wholly untrue' The article went on to claim that Mr al-Amoudi was probably responsible for murdering his daughter's lover in Iraq and had hunted his daughter and granddaughter across London in an attempt to ensure they were stoned to death in Saudi Arabia.
Mr al-Amoudi told the court he was horrified by the "wholly untrue" article which could be seen by visitors to the website between January and August 2010, when it was finally taken down.
Mr al-Amoudi, who has a son and seven daughters, said he had a normal relationship with Sarah, who was not married.
He said she had completed a business administration degree in the UK.
Assessing damages, the judge said: "The claimant is not, I judge, a man who wears his heart on his sleeve.
"But his distress as he described the effect of the article on himself and on his family was evident to me, and the more so because, as it seemed to me, he was doing his best to preserve his composure."
Mr al-Amoudi, who was in the top 50 of Forbes magazine's 2009 rich list, is believed to have made his money in construction, oil refineries and mining.
Mr al-Amoudi, who is of mixed Ethiopian and Arab heritage, is sometimes described as the world's richest black man.
He was recently reported to be financing the building of Saudi Arabia's first car factory.