Fairplex has an existing grandstand, which was built in 1932 and holds 8,000 spectators. It is set to be renovated this year, but is not yet certain if this will be incorporated into stadium plans.
The site has previously held concerts for between 40,000 and 60,000 people.
The International Cricket Council (ICC), International Olympic Committee (IOC) and LA 2028 organising committee worked together over the choice of the venue.
However, it is understood LA 2028 organisers and the IOC had the final say.
ICC chair Jay Shah said he “looked forward to collaborating” with the IOC to make “cricket a huge success there”.
“It will be a fantastic opportunity to expand traditional boundaries when it features in the Olympics in the fast-paced, exciting T20 format that should appeal to new audiences,” said Shah.
The prospect of a temporary venue for matches will once again raise concerns over the use of drop-in pitches.
For the 2024 T20 World Cup, which was co-hosted by the United States, an eye-catching 34,000-seat stadium was built in New York.
However, the drop-in pitches at the Nassau County International Cricket Stadium in Eisenhower Park came under intense scrutiny after they played poorly.
Cricket’s only previous appearance at the Olympics was at Paris 1900, when Great Britain won by 158 runs against France in a one-off final, after the Netherlands and Belgium withdrew.
The England and Wales Cricket Board is understood to have held preliminary talks with Cricket Scotland about plans to field a TeamGB side, with the ICC set to determine the qualification process for the Games.