The list of approved sports includes skateboarding, surfing and sports climbing. All three made successful Olympic debuts in Tokyo and look to be locked in for the future as the IOC chases younger audiences.
It also sets them to receive a share of future Olympic broadcasting income, which is currently worth at least $15 million to each sport.
The three sports left isolated still have a "pathway for inclusion" at the 2023 annual meeting of the IOC membership, Bach said.
They need to "demonstrate to the satisfaction" of the IOC executive board they have made changes variously to the governance and organisational culture of the sports. Modern pentathlon also needs to replace horse riding with a more inclusive discipline accessible to young people worldwide.
Football is still on the Los Angeles program, but Bach put FIFA on notice because of its plans to play World Cups every two years, instead of every four. The current cycle of men's World Cups would put any biennial tournament in a direct clash with the Los Angeles Olympics.
The World Cup plan, which has faced resistance in Europe and South America, is being pushed by FIFA president Gianni Infantino, but momentum has stalled in recent weeks.
Bach said the IOC still had not been consulted about the plan, but he is due to talk Sunday with Infantino — an elected IOC member — at an online meeting of Olympic sports leaders.
Other sports can also be added to the Los Angeles sports program in 2023, when local organisers are scheduled to ask for medal events they want to host. Baseball and softball are a potential choice. They were added by organisers to the Tokyo Olympics, along with karate, to appeal to Japanese fans.
Baseball, softball and karate were not requested by organisers of the 2024 Paris Olympics, which will have breakdancing in addition to skateboarding, surfing and sports climbing.