Miller, who was also managing director of Rugby World Cup Limited, will step down from both roles at the end of January.
The statement did not say who would replace him.
The decision comes one month after Frenchman Bernard Lapasset was re-elected as board chairman.
"Mike will be a hard act to follow. But with my newly re-affirmed four-year mandate, a revamped IRB Executive Committee, a soon to be refreshed Rugby World Cup Board and a vibrant Council and staff we have the tools in place to continue to drive the game forward," Lapasset said in a statement.