The 59-year-old from Germany, a former Olympic fencing champion, won a comprehensive victory over five rivals after a contest which became acrimonious on the eve of the vote in Buenos Aires.
One of Bach's opponents, Denis Oswald from Switzerland, publicly criticised the links between the German and the man regarded as the 'kingmaker' in the IOC, Sheikh Ahmad al-Fahad al-Sabah, from Kuwait.
Oswald was reprimanded for the remark, and it is understood he has since met Bach and they have agreed to put the matter behind them. Britain's IOC member Sir Craig Reedie has spoken glowingly of Bach and called him a "safe pair of hands".
Reedie said: "Winning so convincingly is the ideal way to start what will be a long and difficult job for Thomas Bach.
"I believe this will mean firm leadership and that the Olympic movement is in safe hands."
Asked about Oswald's remarks, Reedie said: "I suspect he will regret saying that now."
Sheikh Ahmad is head of the umbrella group of 205 national Olympic committees called ANOC which has significant influence through administering the Olympic Solidarity fund which has 438million dollars (£300million) to distribute between now and 2016 to needy projects.
Al-Sabah publicly committed himself to supporting Bach, helped Tokyo win the vote for the 2020 Olympics and also backed wrestling to be reinstated as an Olympic sport.
But the Sheikh told reporters in Buenos Aires: "I thank the media for making me a hero.
"But don't hear those rumours. Don't diminish the importance of Dr Bach, he's an athlete with an Olympic gold medal, he's an IOC member more senior than me, he has a lot of relationships, he has built his reputation for a long time, he has been in charge of a main part of the movement. Let's be logical about his experience and his CV."
Bach will succeed Jaques Rogge, who steps down after serving the maximum 12 years in the position.
In his victory address, Bach issued a call for harmony saying: "I would like to thank from the bottom of my heart all my friends and colleagues who voted for me - this is really an overwhelming sign of trust. I also thank my fellow candidates who I greatly respect.
"I will work with you in the coming years and repay your confidence. I know about the great responsibility of an IOC president."
Bach won in the second round of voting with 49 votes beating closest rival Richard Carrion, the Puerto Rican who is in charge of the IOC's finances who polled 29 votes.
Ng Ser Miang from Singapore attracted six votes, Oswald - the Swiss official who oversaw London's preparations for the 2012 Games - received five, and Ukraine's Sergei Bubka four votes after C-K Wu, the Taiwanese head of the international boxing federation AIBA, had been eliminated in the first round.
During the last few days Bach was forced to deny allegations in a German TV documentary about his conduct during his days as a fencer in the 1970s. It accused Bach of wearing a wet glove to fool the electronic scoring system and made other claims about his business activities.
A spokesman for Bach said the claims were "nonsense".