It is a good question. Who approves these transaction? I am by no means an expert and someone with better research skills may better clarify. Is there any congressional oversight
http://www.state.gov/t/pm/rsat/c14021.htm
There is this;
The Foreign Assistance Act (FAA) and the Arms Export Control Act (AECA) vest authority for the sale or grant of USG-origin defense articles, services, and technical data with the President. Executive Order No. 12163 (under State Department Delegation of Authority No. 145, February 4, as amended) granted the Under Secretary for Arms Control and International Security (T) the power to provide consent to these transfers. In 1992 this authority was delegated to the Assistant Secretary for Political-Military Affairs (PM). Since this delegation, PM's Office of Regional Security and Arms Transfers (RSAT) has been charged with handling arms transfers and third party transfers, disposal, and change of end-use involving U.S. -origin equipment procured via the U.S. Foreign Military Sales (FMS) Program and all government to government grant assistance programs. All third party transfer cases undergo an interagency review prior to PM/RSAT’s recommendation of an approval or denial to the PM Assistant Secretary. PM's Directorate of Defense Trade Controls (DDTC) is responsible for authorizing all transfers involving U.S.-origin military equipment acquired through direct commercial sales.
and congressional oversight or approval?
from http://www.state.gov/t/pm/rsat/c14021.htm
Conventional Arms Transfer Policy (CAT)
The Conventional Arms Transfer Policy is the standing Presidential policy guidance on arms transfers. It is guided by two fundamental tenets: to support transfers that meet the legitimate security requirements of our allies and partners in support of our national security and foreign policy interests; and to promote restraint, both by the United States and other suppliers, in transfers of weapon systems that may be destabilizing or dangerous to international peace and security. PM/RSAT is the lead office for implementing the Policy’s guidance.
From what I can see the sales are managed by PM/DDTC
the state dept