AU commission chair Nkosazana Dlamini-Zuma said the threat posed by the Islamist group required a "collective, effective and decisive response".
Boko Haram has seized control of a swathe of north-east Nigeria and killed thousands in a six-year insurgency.
Four of Nigeria's neighbours - Benin, Cameroon, Chad and Niger - have agreed to contribute troops to the task force.
Speaking after AU talks in the Ethiopian capital, Addis Ababa, Ms Dlamini-Zuma said the Multinational Joint Task Force (MJTF) would have an initial mandate of one year.
She said it would conduct "military operations to prevent the expansion of Boko Haram and other terrorist groups' activities and eliminate their presence".
The plan is now expected to be submitted to the UN Security Council for approval.
Institute for Security Studies analyst Liesl Louw-Vaudran said agreement on the force represented a "turnaround" by Nigeria, given its previous opposition to international military intervention.
However, she said it was not yet clear if the MJTF would be deployed as a border force, protecting Nigeria's neighbours from Boko Haram incursions, or whether it would attack the militants inside Nigeria.
'Not doing enough'
Nigeria has insisted that it is capable of tackling Boko Haram and is doing all it can to do so.
However, some of its neighbours, including Niger and Cameroon, have criticised it for not doing enough.
Chadian troops were recently deployed to Cameroon to help repel Boko Haram incursions.
The country's forces have also reportedly been fighting this week in north-east Nigeria, helping to retake the town of Malamfatori from the militants.
It was not clear whether the Nigerian authorities had prior knowledge of, or approved, the cross-border operation.
But late on Thursday, the Nigerian military said Malamfatori was "within the area of operation covered by the MJTF of which Chad has always been a part". It said the Nigerian air force had also been conducting missions in the area for the past two days.
Previous plans to beef up regional forces against Boko Haram have foundered.
Source: http://www.bbc.com/news/world-africa-31057147?ocid=socialflow_twitter
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