The Jawaharlal Nehru Memorial Fund, which awards the fellowship, said Rao will work on a project titled "The Politics of History: India and China, 1949-1962".
Rao served as Foreign Secretary from August 2009 to July 2011. She is the second woman diplomat to become Foreign Secretary after Chokila Iyer.
She had served in various key positions and had been India's envoy to various countries, including the US, China and Sri Lanka.
During her early years in the Ministry of External Affairs, Rao had specialised in India's relations with China, and was a member of the delegation of then Prime Minister Rajiv Gandhi when he made his historic visit to China in 1988.