At 50, Rajan will also be among the youngest to occupy the high office at Mint Street in Mumbai, where he takes over from incumbent Duvvuri Subbarao Sep 5.
"Prime Minister (Manmohan Singh) has approved the appointment of Raghuram Rajan as the Governor of Reserve Bank of India (RBI) for a term of three years,” finance ministry said in a statement.
Before joining the Indian government, Rajan had served as chief economist at the International Monetary Fund (IMF) and professor at the University of Chicago. He joined as advisor in the finance ministry last year in August.
His appointment comes at a time when the Indian economy is passing through rough weather and the government and the central bank are not particularly seen to be in sync on ways to handle the situation.
The RBI is struggling to control the slide in the value of the rupee that hit a record low of 61.86 against a dollar Tuesday.
"These are challenging times for the Indian economy, though no one can have any doubt about the country's promise," he said after being named governor, adding that the government and the central bank were working together on this
"The Reserve Bank is a great institution with a tradition of integrity, independence and professionalism," he said, honoured by the new responsibilities rested on him.
The RBI has also been under pressure from the industry and a section of the government to cut policy rates to revive growth. Rajan has also been advocating a rate cut.
In the first quarter review of the monetary policy announced July 30, the central bank has left key policy rates unchanged and lowered the growth forecast for the current financial year to 5.5 percent from its earlier projection of 5.7 percent.