Basu (60) will begin his term on October 1, World Bank Group President Jim Yong Kim said in a statement.
Basu, who replaces Justin Yifu Lin, was Chief Economic Adviser in India's Finance Ministry till July.
"Having worked in the Ministry of Finance, in addition to his impressive academic achievements, Kaushik is uniquely suited to help us offer evidence-based solutions and advise to client countries and provide innovative excellence in leading our development research," Kim said.
"Kaushik brings the first hand experience from a developing country and will be a terrific asset to the institution," the World Bank statement added.
Basu, who holds a PhD from the London School of Economics, founded the Centre for Development Economics at the Delhi School of Economics in 1992.
He has also published widely and his contributions to the field span development economics, welfare economics, industrial organisation and public economics.
Raghuram Rajan, Chief Economist of IMF, has replaced Basu as India's Chief Economic Adviser.
India's Planning Commission Deputy Chairman Montek Singh Ahluwalia was also associated with the World Bank.
He joined the multilateral institution in 1968 as a Young Professional and then held various positions including Chief of the Income Distribution Division.
Kalpana Kochhar, the Chief Economist for the South Asia Region (Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, and Sri Lanka), is another Indian holding a top position in the World Bank.