Bach, who won fencing gold for West Germany in 1976, finished well ahead of five rivals to claim a convincing election victory at the IOC’s annual session in Buenos Aires.
He becomes the ninth president of the IOC and will serve an initial eight-year term.
Bach, 59, is one of four IOC vice-presidents and was widely considered the frontrunner for the powerful position.
He saw off the challenge of Olympic finance chief Richard Carrion, fellow IOC vice-president Ng Ser Miang, former Olympic pole vault gold medallist Sergei Bubka and executive board members Denis Oswald and CK Wu.
The victory – which was achieved after two rounds of voting – will potentially keep the presidency in European hands for more than 50 years.
“I would like to thank, from the bottom of my heart, all my dear friends and colleagues who voted for me, it’s an overwhelming sign of trust and confidence,” said Bach.
“I also want to thank my fellow candidates, who I greatly respect, and those who didn’t vote for me. I will work for and with you to win your confidence.
“I know about the great responsibility of an IOC president and that makes me humble. I want to lead the IOC according to my motto – unity in diversity.
“I will do my best to balance well all the different interests of the stakeholders of the Olympic movement. I want to listen and enter in an ongoing dialogue with all of you.
“I would like to thank Jacques personally very much. You are leaving such a great legacy and strong foundation to build the future of the IOC.”