Rajan, a high-profile former IMF chief economist renowned for predicting the 2008 global financial collapse, moves into the Reserve Bank of India's office on Thursday, replacing his retiring predecessor Duvvuri Subbarao.
The appointment of the informal, outspoken diplomat's son -- described by the Times of India as an "economist with rock star appeal" -- comes as some analysts fear the once-booming economy could be heading for a meltdown.
India's economy has gone dramatically downhill since the so-called "Indian Summer" -- the heady noughties when growth regularly exceeded eight per cent and the country was a global investor favourite.
Rajan, who qualified as an engineer at the Indian Institute of Technology and later did a management doctorate at the Massachusetts Institute of Technology, faces a virtually impossible "trilemma" in his new job, analysts say.
He inherits an economy with a record current account deficit -- the broadest measure of trade, a currency which has lost 16 per cent against the dollar this year and annual growth at its weakest in a decade at five per cent.
He's "in an unenviable situation," D.K. Joshi, chief economist of leading credit rating agency Crisil, told AFP.
The 50-year-old Rajan cautioned against expecting too much from his appointment -- saying there are no "quick fixes".
"No one can doubt the country's promise," the economist said after being named in early August to the post, but added, "There is no magic wand to make the problems disappear instantaneously".
Analysts have raised fears India could face a crunch of the sort it suffered in 1991 when a foreign exchange-strapped government had to pawn its gold for an International Monetary Fund (IMF) bailout.
Friday's first-quarter figures showing the economy posting an unexpectedly low growth of 4.4 per cent offered no cheer.
"Given the on-going turmoil, economic conditions look likely to get worse before they get any better," said Capital Economics economist Daniel Martin.
For the time being, Rajan, a staunch economic reformer and withering critic of "rampant" Indian corruption and suffocating bureaucracy, will have his hands tied, analysts say.
He will be forced to focus on stabilising the currency by keeping interest rates high at the expense of spurring expansion of Asia's third-largest economy, analysts say.
Meanwhile, the government will have to concentrate on reining in the current account gap which has prompted foreign investors to race for the exits and put pressure on the rupee.
Rajan is known as a "creative, out-of-the-box thinker" which should stand him in good stead, said Deepak Lalwani, head of India-focused financial consultancy Lalcap.
But there is scepticism whether Rajan, even with his strong credentials, can do much to boost the economy. As veteran Indian financial commentator Swaminathan Aiyar remarked: "Great jockey. Pity he doesn't have a better horse."
Rajan won fame as one of the few economists who warned of the global financial crisis before it hit in 2008 when he said sub-prime lending could lead to calamity.
Rajan's dire words earned the scorn of then US treasury secretary Larry Summers who dismissed him as "misguided" and "a Luddite".
The two men now, ironically, may be together soon in the close-working club of global central bank leaders as Summers is frontrunner to be the next US Federal Reserve chief.
Rajan, author of the acclaimed 2011 book Fault Lines on how hidden financial fractures threaten the world economy, left his post as professor at the prestigious University of Chicago's Booth School of Business and returned to India last year.
Rajan, who hails from southern Tamil Nadu state, came at the behest of Indian Premier Manmohan Singh to serve as financial advisor.
Many analysts at the time of Rajan's return speculated his next stop would be the central bank.
"Today's challenges relate to understanding global economic dynamics and Rajan has a big advantage in that department," Siddhartha Sanyal, chief India economist at Barclays Capital, said.
There are observers who suggest that should India's situation unravel further and it has to go to the IMF for help -- a prospect the finance ministry at the moment firmly dismisses -- Rajan's connections with the world body could come in handy.