The official says the agreement would limit each side to 700 armed launchers - such as missiles, bombers or submarines - that are ready to be fired.
President Barack Obama and Russian President Dmitry Medvedev are expected to finalize the agreement in a phone conversation Friday morning.
The agreement would also limit both sides to 1,550 nuclear warheads - a further reduction from previously planned cuts.
The official spoke on condition of anonymity because he was not authorized to speak ahead of the announcement.
The official said the U.S. prevailed in keeping missile defense limitations out of the treaty.