Under the new policy, which takes effect immediately, membership in Cub Scouts and Boy Scouts will be based on the gender indicated on an application.
Previously, the organization relied on an individual's birth certificate to determine eligibility for its single-gender programs.
"However, that approach is no longer sufficient as communities and state laws are interpreting gender identity differently, and these laws vary widely from state to state," BSA spokeswoman Effie Delimarkos said in a statement Monday.
The change brings the Boy Scouts in line with other youth organizations, including the Girl Scouts
, that have created transgender-friendly membership policies in recent years.
It comes a few months after an 8-year-old Cub Scout in New Jersey accused the organization of expelling him for being transgender.
The Boy Scouts did not specifically cite the New Jersey case in its statement. But Chief Scout Executive Michael Surbaugh acknowledged the group recently had been "challenged by a very complex topic... the issue of gender identity."
"We've taken the opportunity to evaluate and update our approach. I hope you'll join with me in embracing the opportunity to bring scouting to more families and children who can benefit from what our organization has to offer," he said in video statement.
"This is an area that we will continue to thoughtfully evaluate to bring the benefits of scouting to the greatest number of youth possible all while remaining true to our core beliefs."
Zach Wahls, co-founder of Scouts for Equality, applauded the decision and credited the New Jersey case with forcing BSA to rethink its policy.
"This is another historic day for the Boy Scouts of America. The decision to allow transgender boys to participate in the Cub Scouts and the Boy Scouts is an important step forward for this American institution," Wahls said.
"We are incredibly proud of Joe Maldonado
-- the transgender boy from New Jersey whose expulsion last year ignited this controversy -- and his mother Kristie for their courage in doing what they knew was right. We are also proud of the Boy Scouts for deciding to do the right thing. We look forward to seeing more detail clarifying this policy change in the days and weeks ahead."
The Boys Scouts of America has come under fire in the past over LGBT issues. In 2015, it lifted the ban on gay adults as Scout leaders. And it was only three years ago that it allowed allowed openly gay youths to join scouting.