Gopinath will succeed Maurice (Maury) Obstfeld, who would retire at the end of 2018, the IMF said.
She currently serves as the John Zwaanstra Professor of International Studies and Economics at Harvard University.
"Gopinath is one of the world's outstanding economists, with impeccable academic credentials, a proven track record of intellectual leadership, and extensive international experience," IMF Managing Director Christine Lagarde said.
Gopinath did her Ph.D. in economics from Princeton University in 2001 after earning a B.A. from the University of Delhi and M.A. degrees from both the Delhi School of Economics and University of Washington.