The delegates "agreed on the need for an immediate, comprehensible ceasefire accompanied by an inclusive political process," a statement read by Said Djinnit, African Union peace and security commissioner, said.
"The proposed operation would contribute considerably to the stabilisation of the situation in Darfur, in its political, humanitarian and security dimensions."
Omar al-Bashir, the Sudanese president, agreed to the package in November, but stalled over the implementation of the two previous stages of the plan.
Bernard Kouchner, the French foreign minister, said on Monday that al-Bashir told him he fully agreed to the proposed hybrid force but was adamant that all of the troops must come from Africa.
The decisions made on Tuesday still have to be approved by the United Nations Security Council and the African Union's Peace and Security Council.
At least 200,000 people have been killed in the conflict in Darfur and two million forced from their homes, according the UN.
Khartoum has disputed the figures saying that just 9,000 people have died since the war started in early 2003 when ethnic minority groups rose up against the government.