As per media reports, the resignation brings to an end his 14-year active stint with India's largest business process outsourcing firm.
Bhasin will now take over as a non-executive vice-chairman of the company, while N V Tyagarajan will succeed as president and CEO.
Tyagarajan, who is currently the chief operating officer (COO), will join the board effective June 17.
He had earlier served as a CEO from 1999 to 2002, when Genpact was a subsidiary of conglomerate General Electric Co .
Genpact was started in 1997 as the India-based business process services unit of GE Capital, General Electric Co's financial services business. GE spun off Genpact in 2005, but remains its largest client.