Kailath, 79, will receive the medal along with nine other awardees, at a White House ceremony later this year.
"These scholars and innovators have expanded our understanding of the world, made invaluable contributions to their fields and helped improve countless lives," Obama said in a press statement.
"Our nation has been enriched by their achievements, and by all the scientists and technologists across America dedicated to discovery, inquiry and invention."
After graduating from the University of Pune in 1956, Kailath received his Master's degree and his doctorate degree in 1961, both from the Massachusetts Institute of Technology US. He was the first India-born student to receive a doctorate in electrical engineering from MIT.
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Born in 1935 to a Malayalam-speaking Syrian Christian family who hailed from Kerala, Kailath has authored several books including well-known Linear Systems.
Kailath's research and teaching at Stanford have covered several fields of engineering and mathematics, with a different focus roughly every decade: information theory, communications, linear systems, estimation and control, signal processing, semiconductor manufacturing, probability and statistics, and matrix and operator theory.
The National Medal of Science was created by statute in 1959 and is administered for the White House by the National Science Foundation.
Awarded annually, the Medal recognises individuals who have made outstanding contributions to science and engineering.