Kony was virtually unknown in the West just weeks ago until a video made by the group Invisible Children about him went viral on YouTube.com.
The group he leads, called the Lord's Resistance Army, is accused of killing hundreds of civilians. Kony is accused of forcing young boys to become soldiers and young girls to become sex slaves.
The African Union mission will be comprise troops from Uganda, South Sudan, the Central African Republic and Congo.
Kony is believed to be hiding somewhere in the Central African Republic. The mission is expected to last until Kony is captured.
The LRA is responsible for 2,600 civilian deaths since 2008, according to the African Union.
The AU's new focus on Kony dovetails with the Ugandan military's stance that catching or killing Kony would mean the end of the LRA. His forces were ousted from Ugandan territory in 2005.
The officials meeting in Uganda on Friday did not say where the funding for the mission was coming from but acknowledged that finding money was a problem.
Kony is wanted by the International Criminal Court for war crimes and crimes against humanity. He is believed to be hiding in the Central African Republic.
The Associated Press contributed to this report.