The members voted 12-0 in favour of signing off on the memorandum of understanding and host city contract documents which would see the city host the Summer Games for the third time in history.
"This opportunity is too great and we cannot pass it up," said council member Herb Wesson.
"We will make the necessary adjustments to make this the most successful Olympics Games in the history of America."
The city council signed off on the Games despite not knowing the full financial reality of hosting the 2028 Olympics.
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Los Angeles started off competing with other cities around the world for the 2024 Games, but eventually all bidders except for Los Angeles and Paris dropped out.
In July, the International Olympic Committee approved the idea of awarding both the 2024 and 2028 Games simultaneously.
The Los Angeles organizing committee proposed a modest budget -- by Olympic standards -- of USD 5.3 billion for 2024 by utilizing existing structures and not building any new permanent venues for the Olympics. The new budget for the 2028 Games is not expected to be ready for months.
The IOC also agreed to waive USD 50 million in fees, contribute up to USD 2 billion of its broadcast and sponsorship revenues to the Games, and channel any of its profits from the Olympics back to Los Angeles.