In June, the International Olympic Committee (IOC) voted to name hosts for successive Games - with just Paris and Los Angeles bidding - but it was unclear which would host in which year.
Both had wanted to host the 2024 event.
The IOC welcomed Los Angeles' move, pledging to contribute $1.8bn (£1.4bn) to the organising committee.
A source close to the negotiations told BBC Sport that for LA to have accepted the 2028 Games there would have had to have been significant financial benefits that outweighed the benefit of hosting in 2024.
The funds will include money to pay for the extended planning period and to support youth sports programmes leading up to the Games.
Los Angeles bid committee chairman Casey Wasserman earlier said "both cities now stand together ready to serve the Olympic and Paralympic movements".
Meanwhile, Los Angeles Mayor Eric Garcetti said "we're bringing the games back" in 2028, adding that "this deal was too good to pass up".
Los Angeles has staged the Olympics twice - in 1932 and 1984.