He takes charge as the central bank grapples with a weakening rupee, a widening current account deficit and a slowdown in economic growth.
India’s currency has declined 20% against the US dollar since May and its growth rate fallen to a ten-year low.
Analysts said that stemming the decline in the rupee would be the first issue that Mr Rajan had to address.
“The rupee will be Rajan’s first and key challenge,” said Vikas Babu Chittiprolu, a senior foreign exchange dealer at Andhra Bank.
For his part, Mr Rajan – known for having predicted the 2008 global financial crisis – has said that “all options were on the table” to stabilise the currency.
“Economic policymakers require an enormous dose of humility, openness to various alternatives (including the possibility that they might be wrong), and a willingness to experiment,” he wrote in a column on the Project Syndicate website last month.
Win back investors
India’s economy has been hurt by a range of factors in recent months. To begin with, its growth rate has been hurt by a slowdown in key sectors such as mining and manufacturing.
In the April-to-June quarter, the economy grew at a rate of 4.4%, compared with the same period in the previous year.
On Tuesday, Goldman Sachs cut its growth forecast for India to 4% from 6%.
At the same time, foreign investors have been pulling out money from the country amid a lack of key reforms as well as improving economic conditions in the US.
Some analysts have said that a slowdown in India’s growth – coupled with a pick up in the US economy, have made the country less attractive to investors.
All of that has hurt the country’s stock market and the currency.
The decline in the rupee especially has stoked fears that India may not be able to trim its current account deficit – a key area of concern among policymakers.
The deficit, which happens when a country’s import bill exceeds the earnings from exports, drains its foreign exchange reserves.
‘Rock star image’
Mr Chittiprolu said that while Mr Rajan’s background of having worked with the International Monetary Fund would be an advantage “he will need to win the market’s faith by announcing something which helps bring in dollar inflows”.
However, Rajeev Malik, a Singapore-based economist, said Mr Rajan’s “rock star academic image could be a hindrance”.
“That is because it has generated unrealistic hope that he has some magical prescription to fix our problems,” he wrote in the Business Standard newspaper on Tuesday.
Mr Rajan is a well-known academic and the author of a prize-winning book, Fault Lines: How Hidden Fractures Still Threaten the World Economy.