Bach, an IOC vice-president, is considered the front-runner in the race to succeed Jacques Rogge, who steps down in September after 12 years as leader of the International Olympic Committee.
The 59-year-old German lawyer, a 1976 Olympic gold medallist in fencing, said he notified Rogge and fellow IOC members of his intention to run on Wednesday. He said he will formally submit his candidacy in June under the motto "Unity in Diversity."
"I didn't want to keep other (IOC) members in the dark any longer," Bach said at a news conference. "I think it is the right time."
Bach, who had been widely expected to run for president, is seen as the favourite among a possible half dozen candidates.
"I am humbly aware of the magnitude of the task of an IOC president," Bach said. "At the same time, in honorary positions and throughout my professional career, I have gained a wealth of management and leadership experience in national and international sports, economics, politics, law and society.
"This is why I feel well prepared."
The German has served on the policy-making IOC executive board as a regular member or vice-president since 1996. As chairman of the IOC juridical commission, Bach leads most of the investigations into doping cases. He also heads the German Olympic Sports Confederation, DOSB.
"My election would be a recognition for German sport," he said.
Bach said he will officially enter as a candidate by the June 10 deadline, exactly three months before the Sept. 10 election in Buenos Aires, Argentina.
"German sport is behind Mr. Bach," DOSB general director Michael Vesper said. "He is an excellent candidate. ... He has demonstrated that he is a real team captain, who seeks dialogue."
An unofficial election campaign has been going on for months, with Bach and other prospective candidates travelling the world to attend various Olympic gatherings to talk to members.
Singapore's Ng Ser Miang, another IOC vice-president, is expected to announce his candidacy soon. Richard Carrion, a former executive board member from Puerto Rico, is another likely leading contender.
Ng led the organizing committee for the inaugural Youth Olympics in Singapore in 2010. Carrion heads the IOC's finance and audit commissions and led negotiations that secured a record $4.38 billion deal with NBC for U.S. TV rights through 2020.
Other likely contenders include Sergei Bubka of Ukraine, the former pole vault champion who still holds the world record in the event, and C.K. Wu of Taiwan, head of the international amateur boxing federation.
Two Swiss members, Rene Fasel and Denis Oswald, have been weighing their options. Fasel is president of the International Ice Hockey Federation. Oswald is the former longtime head of the Association of Summer Olympic International Federations. It's unlikely both will run.
Nawal El Moutawakel, the Moroccan who won a gold medal in the women's 400-meter hurdles at the 1984 Los Angeles Olympics, has also considered a possible run but members say they do not expect her to be a candidate.
AP Sports Writer Stephen Wilson in London contributed to this report.