The organisation, which was founded in 1910, previously only allowed children registered as male on their birth certificate to join their ranks.
The change comes after a transgender eight-year-old was asked to leave the Scouts in New Jersey last year.
But The Boys Scouts of America said the decision was made following discussions nationally on gender identity.
In a statement, The Boy Scouts of America - one of the largest youth organisations in the US - said: "For more than 100 years, the Boy Scouts of America, along with schools, youth sports and other youth organizations, have ultimately deferred to the information on an individual's birth certificate to determine eligibility for our 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."
The move, which comes into force immediately, was welcomed by Zach Wahls, the co-founder of the group Scouts for Equality, who said he was "proud" of the organisation for doing the right thing.
But Kirstie Maldonado, who went public after her son Joe was asked to leave his Scouts group last autumn, said the announcement left her with mixed emotions.
"It's a big change for everybody that all are accepted now... I'm so delighted that they finally called and they did say this, but I'm still angry," she told news agency the Associated Press.
The Boy Scouts of America only lifted its ban on gay members in 2013 - successfully lobbied for by President Donald Trump's pick for secretary of state, Rex Tillerson - and this was followed two years later by a vote to lift the ban on gay leaders.
In the UK, children are already welcome to join Scouts "regardless of their gender identity".
Transgender children who identify as boys are to be allowed to join The Boy Scouts of America for the first time.