A government agency may be established by either a national government or a state government within a federal system. (The term is not normally used for an organization created by the powers of a local government body.) Agencies can be established by legislation or by executive powers. The autonomy, independence and accountability of government agencies also vary widely.

Early examples of organizations that would now be termed a government agency include the British Navy Board, responsible for ships and supplies, which was established 1546 by King Henry VIII and the British "Commissioners of Bankruptcy" established in 1570. The United States Library of Congress was founded in 1800 and is, unusually, an agency of the legislative branch of government.

From 1933, the New Deal saw rapid growth in US federal agencies, the "alphabet agencies" as they were used to deliver new programs mandated by legislation, such as federal emergency relief.

From the 1980s, as part of New Public Management, several countries including Australia and the United Kingdom developed the use of agencies to improve efficiency in public services.

The term agency in India has several meanings; For example, the Cabinet Secretariat describes itself as a "nodal agency for coordination amongst the ministries of the Govt.of India". Most notably as an international feature, what appear to be independent agencies (or apex agencies) include some that have active roles for Ministers: such as, the National Security Council, the Indian Council of Agricultural Research, and the Planning Commission, which is chaired ex-officio by the Prime Minister.

The Government agencies in Sweden are state controlled organizations who act independently to carry out the policies of the Swedish Government. The Government Ministries are relatively small and merely policy-making organizations, allowed to control agencies by policy decisions but not by direct orders. A Minister is explicitly prohibited from interfering with the day-to-day operation in an agency or the outcome in individual cases. While no minister is allowed to give orders to agencies personally, they are subject to decisions made by the Government.

Agencies in the United Kingdom are either executive agencies answerable to government ministers or non-departmental public bodies answerable directly to one of the parliaments or devolved assemblies of the United Kingdom.

Agencies can be created by enabling legislation by the Parliament of the United Kingdom, Scottish Parliament or the National Assembly for Wales.

Agencies in England usually answer to Westminster or the British Government. In Scotland they usually answer to the Scottish Government or the Scottish Parliament and in Wales to the National Assembly for Wales.

Some have remits that cover the entire UK and these organisations are funded by and answer to the British Government.