"It contains aggravating features of exceptional wickedness, which merit exceptional sentences that combine punishment with a clear warning to others who may contemplate similar conduct."
He sentenced five of the youths to 11 years, one to 10 years and another to 12 years. An eighth member of the gang, the 14-year-old "ringleader", is to be sentenced later and was not in court.
Members of their families cried in the public gallery. Also in the gallery was the husband of the victim, although she was not present. Their marriage has broken up, partly because of the attack. During the hearing, an order had banned identification of the teenagers, but the judge yesterday lifted it on four of the gang.
They were the Filipino-born brothers Eduardo Agum, 16, and Allan Agum, 15, of Hackney, east London, Cesar Cardenas, 15, of Clerkenwell, east London, and Nicholas Mavrides, 16, of Camden, north London.
Allan Agum had denied the charge but was convicted at the Old Bailey last week.
The court had heard how the Austrian tourist, an engineer, went for a midnight stroll from her hotel in the King's Cross area of London last September.
She was not worried when first approached by the gang because she thought they were "just babies". But the boys dragged her to a secluded area where they could attack her, ripped her clothes off and raped her one by one. When they were finished, they threw her into the Regent's Canal.
The judge said a particularly offensive aspect of the rape was the "racial element" in the way that the victim was described as a "white bitch".
He told the gang the "aggravating features" of the case were obvious. "There were eight against one; there was a constant repetition of rape; there were other sexual malpractices; there was additional violence; she was forcibly stripped in a most degrading way; there was a racial element to the offence; and finally she was thrown into the water in circumstances which showed that no one cared if she drowned.
"Finally ... when you were all together immediately afterwards, you were laughing and joking about what had happened. It is a terrible story."
The judge said that no one who had listened to the victim's account was ever likely to forget it. He praised her courage but added: "She has suffered since and is suffering still."
The 6ft 2in ringleader, who was living in a children's home, had been already cautioned for theft and carrying an offensive weapon.