Rajan, 50, an economics professor who also served as chief economist at the International Monetary Fund, took charge from D Subbarao.
The duo shook hands warmly and hugged after Rajan signed papers taking over as the 23rd Governor of the central bank.
"Ten minutes ago, I handed over charge to Raghuram Rajan," Subbarao said after stepping out of Mint Road. "The country could not have asked for a more capable person to lead the RBI in these most difficult times.