Kamath will have a five year term of the bank, which is likely to be operationalised within one year, Finance Secretary Rajiv Mehrishi said.
Kamath is the Chairman of the India's largest private sector bank ICICI.
Leaders of the emerging economies of Brazil, Russia, India, China and South Africa (BRICS) had last year reached an agreement to establish the New Development Bank, with its headquarters in Shanghai. As per the agreement, India got the right to nominate the first president.
The BRICS nations account for nearly USD 16 trillion in GDP and 40 per cent of the world's population.
The bank will start with an initial paid-in-capital of USD 50 billion with each BRICS country contributing USD 10 billion.