The draft law was approved in a meeting of Burkina's military-dominated government, according to a statement seen Thursday.
It gave no details about deployment of the force but said these had been determined "by joint agreement" between the two countries.
"What affects security in Niger fundamentally affects security in Burkina Faso," the statement quoted Defense Minister Kassoum Coulibaly as saying.
The bill will be put to Burkina's transitional legislature in the coming days for its approval.
Niger's democratically elected president, Mohamed Bazoum, was toppled by rebel officers on July 26.
They were swiftly supported by juntas in neighboring Mali and Burkina Faso, whose presidents were likewise forced out following failures to stem a jihadist insurgency.
The West African bloc ECOWAS has warned of intervening militarily if diplomatic efforts to return Bazoum to power fail — a move that has prompted Mali and Burkina to say any operation would be tantamount to a "declaration of war" on themselves.
Niger's new strongman, General Abdourahamane Tchiani, last week signed a decree authorizing those countries' forces to intervene "in the event of external armed aggression or destabilization."
Coulibaly, who holds the rank of colonel, said that sending a military contingent to Niger "is a continuation of the struggle against terrorism."
Poorly equipped, the armed forces in all three Sahel countries have been struggling against a jihadist campaign that flared in northern Mali in 2012 and three years later moved into Niger and Burkina Faso.
Across the region, thousands of civilians, police and troops have been killed.
In Burkina Faso alone, which underwent two coups last year, more than two million people have fled their homes and at least a third of the country lies outside the government's control.