The summit was expected to formally announce its decision later on Friday, but a copy of the agreed resolution was obtained by the Reuters news agency.
"[The AU] decides that in view of the fact that a request of the African Union [to defer al-Bashir's indictment] has never been acted upon, the AU member states shall not co-operate persuant to the provisions of Article 98 of the Rome Statute of the ICC relating to immunities for the arrest and surrender of Sudanese President Omar al-Bashir to the ICC," it said.
'New world terrorism'
The UN Security Council can ask the court, via a resolution, to suspend investigations or prosecutions for 12 months, under Article 16 of the Rome Statute.
The text was backed by Muammar Gaddafi, the Libyan leader and current AU chief, who has said the international court in The Hague represents a "new world terrorism".
Gaddafi's position has received widespread support from many countries who felt the court was unfairly targeting Africans.
"We have been a little unhappy about the whole process, how this matter came before the ICC," Alhaji Muhammad Mumuni, Ghana's foreign minister, said before the final decision was taken.
"The AU actually addressed a resolution to the security council asking the SC to defer the warrant for one year, and it was virtually ignored. That we thought was a slap," he said.
"We thought that as Africans, and having a clear understanding and a clear interest in the interest of peace in the Sudan and in Darfur, we thought that was a matter [where] the Security Council should have listened to Africa, at the very minimum."
Al-Bashir was indicted over his alleged role in the conflict in the western Sudanese region of Darfur, which the UN says has killed up to 300,000 people and displaced an estimated 2.7 million.
Khartoum disputes the figures saying that only 10,000 people have died since ethnic minority fighters rose up against the Arab-dominated government and its allies.