Wu, a 66-year-old architect from Taiwan who has been International Amateur Boxing Association president since 2006, said he is declaring his candidacy to "positively impact society."
"Now that the time has come, I am ready to step up," Wu said. "The thought and concept to develop the IOC and Olympic movement ... is the core principle of my candidature.
"The IOC and the Olympic Games have more power to positively impact society than any other organization and project in the world."
Wu joins IOC vice presidents Thomas Bach of Germany and Ng Ser Miang of Singapore, and Richard Carrion of Puerto Rico as candidates in the race to replace Rogge, a Belgian orthopedic surgeon who will step down in September after 12 years.
Sergei Bubka of Ukraine is also expected to run. The election is set for Sept. 10 in Buenos Aires, Argentina.
Wu declined to speculate on his chances for election, except to say that he is popular among IOC members.
"I will do my best to convince the members that I am a capable candidate," he said.
Wu said that if his candidacy succeeds, he will make an effort to promote education as a way to combat the scourges of doping, gambling, match-fixing and violence in sports.
"I strongly urge that we concentrate more on education than ever before," he said. "I truly believe that there is no better solution to fighting against these problems than providing young people with education early on."
Wu, an IOC member since 1988, was elected to the IOC's policy-making executive board last year and was a member of the IOC coordination commissions for the 1998 Winter Games in Nagano, Japan, and 2008 Beijing Olympics. He currently sits on the coordination panel for the 2016 Olympics in Rio de Janeiro.
Last month, Wu hosted numerous IOC members in Tianjin, China, for the opening of a museum he designed to honor late IOC President Juan Antonio Samaranch.
Last week, AIBA's executive committee recommended that Wu run for IOC president.
Wu's native Taiwan competes in the Olympics under the name Chinese Taipei, to distinguish it from mainland China. Taiwan and China split amid civil war in 1949, and while both participated in the 1952 Summer Games in Helsinki, Finland, China subsequently withdrew to protest Taiwan's inclusion in the Olympics.
China returned to the Winter Games in 1980 and the Summer Games four years later after the IOC formally adopted the Chinese Taipei moniker to describe Taiwan.
Wu paid tribute to Samaranch and Rogge in a statement released Thursday.
"I truly believe that no other individual, including me, will ever be able to lead the Olympic movement the way they did. These two leaders have made of the IOC a true leading organization that contributes to offering welfare and bright hopes to every mankind," Wu said. "The days of the IOC renaissance have certainly arrived.
"Therefore, I truly believe that the IOC now needs a leader who is able to harmonize all relationships, delegate his responsibilities to the members and support them in the realization of the Olympic ideals and beyond."