An IMF veteran Singh had earlier served as special advisor to the Governor of the Reserve Bank of India (RBI).
Singh, director of the Asia and Pacific Department at the IMF, has notified managing director Christine Lagarde of his intention to retire from the fund in coming months.
"Anoop's departure will deprive the fund of one its most distinguished staff members, and his friends of a hugely admired colleague," Lagarde said in a statement.
The IMF chief said that Singh had played a critical role during the Asian crisis of the late 1990s.
"Anoop charted a very successful path of engagement with our members in the region at a time when the world economy became engulfed in crisis. We thank him for his outstanding contribution to the fund and the international community," Lagarde said.
Singh, the statement said, has made major academic and policy contributions on various issues, in the process helping to design key Fund-supported programs in emerging market, transition, and developing countries in South and South-East Asia, Eastern Europe, and Latin America.
He joined the IMF Economist Programme in 1973 and has served in various positions, including as Director of the Western Hemisphere Department and as the Fund's Resident Representative in Sri Lanka.
Recently, he also taught courses at Georgetown University. He holds degrees from the universities of Bombay and Cambridge, and the London School of Economics.