The decision came after Nigeria's President Muhammadu Buhari rejected calls for a rotating command between the partners, arguing it could hamper the counter-insurgency effort.
Buhari has made ending the six-year Islamist insurgency his top priority but since coming to power on May 29, more than 150 people have been killed in an upsurge of attacks.
In the latest sign of the need for an enhanced force against the rebels, residents said 43 people were killed in raids on three villages in Borno state in Nigeria's restive northeast.
Cameroon will take the number two role of "deputy first commander" for an initial 12 months while a Chadian will be appointed chief of staff, again for the first year, the statement said.
"National contingents" of troops for the Multi-National Joint Task Force (MNJTF) from Nigeria, Cameroon, Chad, Niger and Benin should be deployed by July 30, it added.
The MNJTF will replace an existing ad hoc coalition of Nigeria, Niger, Chad and Cameroon, which has claimed a series of successes against Boko Haram since February.
Nigeria's military last week announced that Major-General Tukur Buratai had taken charge of the MNJTF, which has its headquarters in Chad's capital, N'Djamena.
The headquarters will cost $30 million (27 million euros) to run in the first year.
Buhari earlier told his regional counterparts and Cameroon's defence minister, representing President Paul Biya, that there was a need to view the insurgency as part of the "global war against terror".
The regional meeting was being closely watched for indications about the extent to which foreign forces can operate inside Nigerian territory.