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Anderson received his Ph.D. at Johns Hopkins University in 1907, and remained on the staff after graduation. In 1908 he became professor of astronomy at the university. In 1909 he was also given the responsibility for the Rowland ruling engines that were used for creating diffraction gratings, and the quality of these was considered excellent, especially the concave gratings.
In 1916 he left to work at the Mt. Wilson observatory. He remained on the Mt. Wilson staff until 1956. His most notable contribution was his adaptation of the Michelson's interferometer technique for measuring close double stars. He used a rotating mask at the focus to measure the separation of Capella.
From 1928 until 1948 he was Executive Officer of the Caltech Observatory Council, working on the instrument and optical design of the main Palomar Observatory telescope. During this period he collaborated closely with George E. Hale and the Rockefeller Foundation.
Unless otherwise noted, the following publications were by John A. Anderson.
- "On the Application of the Laws of Refraction in Interpreting Solar Phenomena", Astrophysical Journal, vol. 31, 1910.
- "A method of investigating the Stark effect for metals, with results for chromium", 1917.
- "The vacuum spark spectrum of calcium", 1924.
- "The Use of Long Focus Concave Gratings at Eclipses", Publications of the Astronomical Society of the Pacific, Vol. 38, 1926.
- J. A. Anderson and Russell W. Porter, "Ronchi's Method of Optical Testing", Astrophysical Journal, vol. 70, 1929.
- "Spectral energy-distribution of the high-current vacuum tube", 1932.
- "On the application of Michelson's interferometer method to the measurement of close double stars", Astrophysical Journal, vol. 51, June 1920.
- "Optics of the 200-inch Hale Telescope", Publications of the Astronomical Society of the Pacific, Vol. 60, 1948.
- Bowen, Ira S. (1962). "John August Anderson 1876–1959" (PDF). Biographical Memoir. National Academy of Sciences, Washington D.C. Retrieved 15 March 2018.