The German became only the ninth president in the body's 119-year history after succeeding Belgium's Jacques Rogge who stepped down after 12 years at the helm.
"I want to be president of all of you," the German beamed as his fellow IOC members applauded the decision.
Bach, a firm favourite in a choice of six candidates, secured victory in the second round of voting.
He polled 49 of the available 93 votes, beating Puerto Rican Richard Carrion into second place on 29 votes.
Bach, long the front-runner for the top job, ticked all the boxes. An Olympic fencing champion at the 1976 Games, the multi-lingual and affable German was the founding president of his country's Olympic Sports Confederation with some 28 million members.
Sitting on the boards of several companies, Bach is also the chairman of the Ghorfa Arab-German Chamber of Commerce and Industry, and his involvement with the Olympic movement stretches back to the milestone Olympic congress in Baden-Baden where he became a representative of the athletes.
As head of the IOC's juridical commission and its disciplinary commission Bach has also been at the forefront of sanctioning drugs cheats, in line with Rogge's "zero tolerance" policy.