The Academy was founded in 1934 by Professor C. V. Raman (Nobel Laureate) and was registered as a Society under the Societies Registration Act, on 24 April 1934. The formal inauguration took place on 31 July 1934 with 65 Founding Fellows. On the same day, the first general meeting of Fellows was held at which C. V. Raman was elected its President, and the draft constitution of the Academy was approved and adopted. The first issue of the Academy "Proceedings" appeared in two sections in July 1934. Since then, the "Proceedings" were split into theme journals and several new ones added.

The Academy presently has 1010 Fellows, 52 Honorary Fellows, and 53 Associates on its rolls.

Past Presidents:

• C. V. Raman (1934 - 1970)
• Prof. T. S. Sadasivan (1971 - 1973)
• Prof. M. G. K. Menon (1974 - 1976)
• Prof. S. Dhawan (1977 - 1979)
• Dr. S. Varadarajan (1980 - 1982)
• Prof. S. Ramaseshan (1983 - 1985)
• Prof. O. Siddiqi (1986 - 1988)
• Prof. C. N. R. Rao (1989 - 1991)
• Prof. R. Narasimha (1992 - 1994)
• Prof. P. Rama Rao (1995 - 1997)
• Prof. N. Kumar (1998 - 2000)
• Dr K. Kasturirangan (2001 - 2003)
• Prof. T. V. Ramakrishnan (2004 - 2006)
• Prof. D. Balasubramanian (2007 - 2009)
• Prof. A. K. Sood (2010 - 2012)