Upon receiving his MSEE from Purdue, George E. Mueller began his career as a researcher with Bell Laboratories. He also worked as a professor of electrical engineering at Ohio State University for 10 years and was one of the originators of the concept and design of the Telebit digital telemetry system.

While associated with Space Technology Laboratories (now TRW), Mueller was responsible for the design, development, and testing of systems and components of the Atlas, Titan, Minuteman, and Thor ballistics missile programs. He also played a major role in the development of the space probe, Pioneer I, and the establishment of the U. S. Air Force SPAN satellite tracking network. From the beginning of Gemini flight operations in 1963 through the second Apollo moon landing in 1969, Mueller directed the U. S. manned flight program as associate administrator for Manned Space Flight with the National Aeronautics and Space Administration (NASA). Mueller served as senior vice president of General Dynamics until 1971 when he was named chairman of the board and chief executive officer of System Development Corporation in Santa Monica. Mueller is a Fellow of the American Association for the Advancement of Science, the American Geophysical Union, the American Astronautical Society, the Institute of Electrical and Electronics Engineers, and the Aeronautical Society. He is an honorary Fellow of the American Institute of Aeronautics and Astronautics and of the British Interplanetary Society.

He holds the Goddard Award from the American Institute of Aeronautics and Astronautics, the National Medal of Science for his contributions to the Apollo System, and three NASA Distinguished Service medals. Mueller has received six honorary doctorate degrees including one awarded to him by Purdue University in 1965.