Bolton has been accused since October of storing top-secret documents at home and of sharing classified information with relatives.
The indictment includes 18 counts.
The agreement with the Justice Department, which has not been made public, will see Bolton face a maximum sentence of five years in prison. But the judge could also decide not to impose any prison sentence, the AP's source said.
However, Bolton is expected to be fined $2.25 million, according to the information.
Bolton was national security adviser for just under a year and a half during Trump's last term. In recent years, he has positioned himself as a vocal Trump critic.
