The special investigation team (SIT) would seize “black money” – cash that has not been declared or taxed and is mostly deposited in foreign banks.
The decision was taken at the first cabinet meeting of the new government.
According to some estimates, some $500bn (£297bn) is deposited in overseas tax havens.
In January, the country’s central bank announced the withdrawal of all currency notes printed prior to 2005 from 31 March in a bid to curb the circulation of black money.
The SIT on black money would be led by retired Supreme Court judge MB Shah and its vice-chairman would be another former judge, Arijit Pasayat, the new Law and Telecoms Minister Ravi Shankar Prasad.
Speaking after Tuesday evening’s cabinet meeting, Mr Prasad said “unearthing black money was an important issue” for the new government.
In the past, officials have said that illegal funds were often sent to tax havens such as Mauritius, Switzerland, Lichtenstein and the British Virgin Islands, among others.
Analysts say this flight of capital has helped widen inequality in India.
The former Congress party-led government had been on the back foot on the issue of black money and corruption.
The Supreme Court has also chided the government for not doing enough to unearth illicit money.