The 34-year-old will be allowed to study certain modules, but will not be admitted to the degree programme, as he at present lacks the necessary qualifications.
He will not be permitted to enter the university campus, studying instead from a room in the prison, without access to the internet.
"Norwegian law recognises that all detainees have the right to work and study," said Karl Gustav Knutsen, warden of Skien Prison in southeast Norway, where Breivik is held.
Ole Petter Ottersen, the university's rector, on Tuesday night wrote an eloquent defence of the decision, arguing that "it demonstrates is that our values are fundamentally different from his".
Writing on the Guardian newspaper's Comment is Free page, he said allowing a man who had committed such heinous acts to study was in keeping with "the calm and reasoned way" in which his case was tried in court.
"We do acknowledge that there are moral dilemmas in this case, but the last thing we need is a "lex Breivik"," he wrote. "We keep to our rules for our own sake, not for his."
He said that he hoped that Breivik's study would give him cause to question the anti-Islamic ideology that lay behind his acts:
"Having been admitted to study political science, Breivik will have to read about democracy and justice, and about how pluralism and respect for individual human rights, protection of minorities and fundamental freedoms have been instrumental for the historical development of modern Europe."
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According to Vibeke Hein Bæra, Breivik's lawyer, he intended to two subjects out of the three he had originally selected, which were political theory, international politics, and public administration.
"Breivik does not deserve to be able to study anything," Ingrid Nymoen, a survivor of the Utøya shooting, said on Twitter.
Breivik killed 77 people in 2011 when he mounted a twin terror attack, detonating a bomb under the main government building and then shooting 69 people at a Labour party youth camp.