The Federal Aviation Act of 1958 created what was then known as the Federal Aviation Agency (FAA). This was changed to the Federal Aviation Administration (still the FAA) in 1966 when it became a part of the US Department of Transportation (DOT).
The FAA's predecessor, the Civil Aeronautics Administration (CAA) was established in 1940 by President Roosevelt, when he split the Civil Aeronautics Authority in two, to create the CAA and the CAB (Civil Aeronautics Board). The CAA was created in 1938 by the Civil Aeronautics Act.
Prior to this, the Air Commerce Act of 1926 created an aeronautics branch of the Department of Commerce. This was the first Federal Act that regulated aircraft and pilots in the United States and began regulatory oversight over those entities.