The German becomes the eight European leader of IOC.
The victory was released in an Olympic Website, “Inside the Games’’, monitored in Lagos.
Rogge, who spent 12 years at the top of the Olympic Movement announced that the members had elected the new president after two rounds of voting in which Bach polled a majority 49 votes.
He finished ahead of Puerto Rico’s Richard Carrion with 26, Singapore’s Ser Miang Ng, six, Switzerland’s Denis Oswald, five and Ukraine’s Sergey Bubka, four.
An announcement made at a special ceremony in Buenos Aires’, Hilton Hotel, venue of the election, said the 59-year-old lawyer, the long-time favourite to succeed Rogge, was officially unveiled.
The IOC members then elected a winner in the next round with only Bach having enough support to win so early, ahead of the rest of the field.
Bach’s election means that the most powerful position in world sport will remain in Europe.
The 1976 Olympic fencing gold medallist will become the 9th President of the IOC since it was founded in 1894 – and the eighth European.
The only non-European was American Avery Brundage, who held the position between 1952 and 1972.
“I would like to thank all my dear friends and colleagues who voted for me this morning,’’ said Bach after Rogge had opened the envelope and read out his name.
“This is an overwhelming sign of trust and confidence. I would like to thank my fellow candidates, who I respect, and those who did not vote for me.
“I want to win your confidence too. I know about the great responsibilities of the job – this makes me humble.
“I want to lead the IOC by my motto, unity in diversity, I want to be a President for all of you.
“I will do my best to balance well the interests of all the stakeholders of the Olympic Movement. My door, ears and heart are always open to you.’’
Rogge, who is also resigning as a member of the IOC following this Session, was presented with the Olympic Order by Bach.
“Dear Jacques, I’d like to thank you,’’ Bach said, adding, “You are leaving such a legacy and a strong foundation on which we can continue to build the future of the IOC.”
“I would like to thank you for the trust you have placed in me for 12 years of your presidency. I hope I can count on your good advice in the years to come.’’