Bach, a 59-year-old German lawyer, was elected Tuesday as president of the International Olympic Committee. He succeeds Jacques Rogge, who stepped down after 12 years.
Bach, the longtime favourite, defeated five candidates in a secret ballot for the most influential job in international sports, keeping the presidency in European hands.
The former Olympic fencer received 49 votes in the second round to secure a winning majority. Richard Carrion of Puerto Rico finished second with 29 votes.
One of the first congratulatory phone calls came from Putin, who will host the IOC in less than five months at the Winter Olympics in the southern Russian resort of Sochi.
The Sochi Games are one of Putin's pet projects, with Russia's prestige on the line.
"He congratulated and (said) there would be close co-operation to make (sure of) the success of the Sochi Games," Bach told The Associated Press.
The buildup to the Feb. 7-23 games has been overshadowed by concerns with cost overruns, human rights, a budget topping $50 billion, security threats and a Western backlash against a Russian law against gay "propaganda."
Bach and the IOC have been told by the Russians there would be no discrimination against anyone in Sochi, and that Russia would abide by the Olympic Charter.
"We have the assurances of the highest authorities in Russia that we trust," Bach said.
It remains unclear what would happen if athletes or spectators demonstrate against the anti-gay law. Rogge said this week the IOC would send a reminder to athletes that, under the Olympic Charter, they are prohibited from making any political gestures.
"We will work on our project now and then it will be communicated to the NOCs (national Olympic committees) and then athletes," Bach said. "It will be elaborated more in detail."
At his first news conference as president, Bach was asked about how the IOC would deal with human rights issues in host countries. The IOC has been criticized for not speaking out against abuses in countries like China and Russia.
"The IOC cannot be apolitical," Bach said. "We have to realize that our decisions at events like Olympic Games, they have political implications. And when taking these decisions we have to, of course, consider political implications.
"But in order to fulfil our role to make sure that in the Olympic Games and for the participants the Charter is respected, we have to be strictly politically neutral. And there we also have to protect the athletes," he said.
A former Olympic fencing gold medallist who heads Germany's national Olympic committee, Bach is the ninth president in the 119-year history of the IOC. He's the eighth European to hold the presidency.
Of the IOC's leaders, all have come from Europe except for Avery Brundage, the American who ran the committee from 1952-72.
Bach is also the first gold medallist to become IOC president. He won gold in team fencing for West Germany in the 1976 Montreal Olympics.
He received a standing ovation for nearly a full minute after Rogge opened a sealed envelope to announce his victory. Bach bowed slightly to the delegates to acknowledge the warm response and thanked the members in several languages.
"This is a really overwhelming sign of trust and confidence," Bach said.
"I want to be a president for all of you," he told the members. "This means I will do my very best to balance well all the different interests of the stakeholders of the Olympic movement. This is why I want to listen to you and to enter in an ongoing dialogue with all of you. You should know that my door, my ears and my heart are always open for you."
Bach was viewed as the favourite because of his resume: former Olympic athlete, long-serving member of the policy-making IOC executive board, chairman of the legal commission, head of anti-doping investigations and negotiator of European TV rights.
"It is what I and many of the others had anticipated," said IOC member Prince Albert of Monaco. "I think it was very clear. You can't argue with his experience and his leadership and his great knowledge about the Olympic movement and the world of sports, and also the outside world. I think we are getting a great president."
Bach was elected to an eight-year term. In 2021, he would be eligible to run for a second and final four-term term.
Bach presented the 71-year-old Rogge with the IOC's highest award, the Olympic gold order.
After awarding the 2020 Olympics to Tokyo and bringing wrestling back into the games, the IOC completed the last of its three critical votes — choosing the person to lead the body for the most powerful job in international sports.
Bach's supporters had hoped for a first-round win, but a second-round victory still showed that he had a big base of support.
Carrion, who chairs the IOC's finance commission and negotiates lucrative U.S. TV rights deals, wound up being Bach's only serious challenger.
The votes fell off after that with Ng Ser Miang of Singapore getting six, Denis Oswald of Switzerland five and Sergei Bubka of Ukraine four. C.K. Wu of Taiwan was eliminated in the first round after an initial tie with Ng as low vote-getter.
In the first round, Bach got 43 votes, followed by Carrion with 23, Bubka eight, Oswald seven and Ng and Wu six each. Ng then beat Wu 56-36 in a runoff.
Ng had been considered a strong contender, but his chances were dented after Tokyo's win because the IOC was unlikely to give Asia two major prizes in a row.
Much of the pre-election talk among the members has been about the power of Sheik Ahmad Al-Fahad Al-Sabah, the Kuwaiti who heads the Association of National Olympic Committees.
The sheik was a key backer of Bach. With his influence in Asia and among the national Olympic committees, the Kuwaiti was seen as playing a key role in Tokyo's victory, even helping Istanbul get to the second round of voting to keep Madrid out of the final.
AP Sports writers Stephen Wade and Tales Azzoni contributed to this report.
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