Barron and his mother Melania, Mr Trump's third wife, are expected to leave Trump Tower in New York after the end of the current school year.
He will go to St Andrew's Episcopal School in Maryland, where tuition costs almost $40,000 (Â£31,000) per year.
There had been questions about when the First Family would move to Washington.
Mrs Trump said in a statement that St Andrew's was "known for its diverse community and commitment to academic excellence", adding: "We look forward to the coming school years."
Barron will be the first child of a president to attend the school, which is a 30-minute drive from the White House.
St Andrew's has refused to comment on their newest student, citing reasons of privacy.
Recent First Daughters such as Sasha and Malia Obama have attended Sidwell Friends, a Quaker school with campuses in Washington and Maryland.
The White House announcement comes after St Andrew's sent a letter to parents on Friday, informing them of the First Family's decision.
St Andrew's had intended to wait until the summer to make the announcement in order to stave off possible protests while school was in session, the Washington Post reports.
But after parents began to hear rumours, the school sent out a letter, prompting Monday's statement from the White House.
Melania, Ivanka and Barron Trump - who is the new first family?
Barron Trump, US President Donald Trump's 11-year-old son, will attend a school outside Washington when he moves into the White House this summer.