user: Article:Breivik, who admitted killing 77 people when he bombed central Oslo and then opened fire at an island youth camp, told the court he would not appeal.
He insisted he was sane and refused to plead guilty, saying last year's attacks were necessary to stop the "Islamisation" of Norway.
Prosecutors had called for him to be considered insane.
Breivik was convicted of terrorism and premeditated murder, and given the maximum sentence of 21 years' imprisonment.
However, that can be prolonged at a later date if he is deemed to remain a danger to society.
By Lars  BevangerBBC News, Oslo
Many relatives and survivors reacted with relief as Judge Wenche Arntzen declared Anders Breivik to be sane, sentencing him to at least 21 years in prison.
The mother of one 16-year-old girl who Breivik shot dead on Utoeya island said she felt "a little happiness" at the fact he was found to be sane.
Still, she said, she had wished he could have been sentenced to 21 years in prison for each of the 77 lives he took.
Others said Breivik the man had for some time now been irrelevant to them, and that the outcome of the trial could never bring their loved ones back.
Survivorsâ€™ relief over sentence
Delivering the verdict, Judge Wenche Elisabeth Arntzen said that the court considered Breivik to be suffering from "narcissistic personality characteristics" but not psychosis.
She imposed a sentence of "preventive detention", a special prison term for criminals considered dangerous to society.
She set the minimum length of imprisonment to 10 years.
Afterwards Breivik said he did not recognise the court, which he contended had "sided with the multicultural majority in parliament", but said he would not appeal as this would legitimise the proceedings.
Prosecutors - who had argued the defendant was insane - also said they would not challenge the verdict.
Some of the survivors and relatives of his victims welcomed the verdict and the end of the trial.
"Now we can have peace and quiet," Per Balch Soerensen, whose daughter was among those killed in the shootings on on Utoeya island, told Denmark's TV2.
"He doesn't mean anything to me; he is just air."
Court-appointed psychiatrists disagreed on Breivik's sanity. A first team which examined him declared him to be a paranoid schizophrenic, but the second found he was sane.
Breivik verdict: Norwegians react
Norway attacks: The victims
How the attacks unfolded
Before the verdict, Breivik said psychiatric care would be "worse than death".
He will serve his sentence at Oslo's high-security Ila Prison, where he has been held in isolation for most of the time since his arrest.
Initially he will be kept isolated from casual contact with other prisoners.
Breivik, 33, carried out the meticulously planned attack on 22 July 2011, wearing a fake police uniform, and methodically hunted down his victims.
He accused the governing Labour Party of promoting multiculturalism and endangering Norway's identity.
Some victims at the Labour Party youth camp on Utoeya island were shot in the head at point-blank range.
Ahead of the verdict, security barriers were put up outside the district court in Oslo.
A glass partition separated Breivik from relatives of victims in a courtroom custom-built for the trial.
Remote-controlled cameras filmed the proceedings, sending the images to courtrooms around Norway where other relatives could watch the hearing live.
Breivik's trial, which began in March and lasted for 10 weeks, heard graphic testimony from some of the survivors of his attacks.
Mohamad Hadi Hamed, 21, who is now in a wheelchair, told the court how his left arm and his left leg were amputated after he was shot by Breivik.
Another survivor, Einar Bardal, 17, described how he was trying to escape when he heard a loud bang, followed by a loud noise in his head.
Experts in far-right ideology told the trial Breivik's ideas should not be seen as the ramblings of a madman.
Breivik's attacks ignited a debate about the nature of tolerance and democracy in Norway.

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assistant: A Norwegian court has found that mass killer Anders Behring Breivik is sane and sentenced him to 21 years in jail.