Actor Tom Cruise descended from the roof of Stade de France to collect the Olympic flag as part of the handover to the American city of Los Angeles, which will host the next Games in 2028, before departing on a motorcycle.
Red Hot Chili Peppers, Billie Eilish, Snoop Dogg and Dr Dre then performed on Venice Beach as part of a star-studded music set to conclude the ceremony.
Earlier, inside the stadium in Paris, gold medallists Alex Yee and Bryony Page were Great Britain's flagbearers at the ceremony.
Bach, who will step down as IOC president in 2025, said Paris 2024 had been "sensational, or dare I say, 'Seine-sational'" - a play on words referencing the river which flows through the host city.
He added that they were "Olympic Games of a new era" as the first "delivered completely under our Olympic agenda reforms: younger, more urban, more inclusive, more sustainable and the first Olympic Games with full gender parity".
The German praised athletes for their "simply amazing" performances, saying they showed "what greatness we humans are capable of".
He continued: "During all this time, you lived peacefully together under one roof in the Olympic Village. You embraced each other. You respected each other, even if your countries are divided by war and conflict. You created a culture of peace.
Yee won the men's triathlon in dramatic fashion, while Page won Britain's first ever Olympic trampoline gold.
Great Britain finished seventh in the medal table with 14 gold, 22 silver and 29 bronze. Their final tally of 65 medals was one more than the 64 they won at Tokyo 2020.
In his closing speech, International Olympic Committee (IOC) president Thomas Bach reflected on a "sensational" Games.
The 2024 Paralympics will be held in the French capital from 28 August to 8 September.
This inspired all of us and billions of people around the globe. Thank you for making us dream. Thank you for making us believe in a better world for everyone.
"We know that the Olympic Games cannot create peace. But the Olympic Games can create a culture of peace that inspires the world. This is why I call on everyone who shares this Olympic spirit: let us live this culture of peace every single day."
There was also special praise for the 45,000 volunteers who assisted during the Games, which began with a rain-soaked opening ceremony along the Seine on 26 July.
Mountain biker Kate Courtney, track and field legend Michael Johnson and skateboarder Jagger Eaton took the Olympic flag on a tour of the city - visiting sites such as the Los Angeles Memorial Coliseum and Venice Beach - while Cruise was pictured in front of the iconic Hollywood sign, complete with Olympic rings.
Rapper Snoop Dogg, who has been working as a special correspondent for American television network NBC during Paris 2024, performed alongside Dr Dre as part of a memorable finale that whetted the appetite for four years' time.
As well as reflecting on the Olympics in Paris, the closing ceremony provided a showcase for Los Angeles, which will host the Games for a third time in 2028.
R&B artist H.E.R. performed the American national anthem inside Stade de France before viewers were transported to LA.