"New times are calling for new leaders," the 70-year-old German lawyer, who has been in charge since 2013, told a session of IOC members in the French capital.
Bach said he was asked to stay in his role but insisted he would not attempt to extend his mandate by changing the Olympic charter that limits the president to a maximum of 12 years in the role.
"I know with this decision I am disappointing many of you....but it is in the best interests of our beloved Olympic movement," he said.
His successor will be elected in 2025.
The jostling to succeed Bach will now begin, with some well-informed IOC watchers tipping Zimbabwean former swimmer Kirsty Coventry for the role.
