A statement on jihadist websites said the attacks Sunday night, on the high-security Taji and Abu Gharib prisons on the outskirts of Baghdad, had been planned for months.
The coordinated attacks, which included car bombs, missiles and mortar rounds, freed at least 500 mujahedin, or "holy warriors,' the website said.
At least 25 prison guards were killed, The New York Times reported.
The brazenness of the assaults underscored the deterioration of Iraq's stability in recent months. Car bombings and other violence, tied to a rebirth of sectarian fighting, is almost a daily occurrence, the newspaper noted.
The day before the bombings, tribal leader Sheik Abdallah Sami al-Assi was assassinated, with two of his bodyguards, in the northern Iraq city of Kirkuk. A statement by the United Nations Tuesday strongly condemned the killings, calling al-Assi a "pivotal and well-respected political figure in Kirkuk."