The new policy was approved 45-12 votes by the BSA's National Executive Board.
Church-sponsored Scout units are allowed to exclude LGBT leaders for religious reasons.
There has been concern from a number of groups that sponsor units, including the Roman Catholic church and the Southern Baptist Convention, about ending the ban on gay adults.
However, the Human Rights Campaign, an LGBT-rights group, has stressed the Boy Scouts should not allow the church to exclude gay leaders.
"Discrimination should have no place in the Boy Scouts - period," said HRC president, Chad Griffin.
"BSA officials should now demonstrate true leadership and begin the process of considering a full national policy of inclusion."
The new policy lets local units to decide on adult leaders without looking into their sexual orientation - a stance that several Scout councils had already been using.
In 2013 after a debate the BSA decided to admit openly gay youths as Scouts, but not gay adults as leaders.
After the 2013 decision to admit LGBT youth, some conservatives split from the BSA to form a new group, Trail Life USA, which has created its own ranks, badges and uniforms.
The group says more than 25,000 youths and adults are now members.
The Boy Scouts currently has around 2.4 million boys and one million adult members.
