The 66-year-old German was elected for an eight-year term as Olympic chief in September 2013. He will be eligible for a second four-year term.
Speaking at the 136th IOC Session, held virtually because of the coronavirus pandemic, Bach said: "If you, the IOC members, want, I am ready to run for a second term as IOC president and to continue to serve you and this Olympic movement we all love so much for another four years."
The IOC presidential elections are slated to take place in Athens in June 2021.
Bach, who won gold for West Germany in the foil fencing team event at the 1976 Olympics, claimed a large number of IOC members had recently approached him asking if he would seek re-election.
"I am grateful and deeply touched by the many words of encouragement and confidence," Bach said.