Across the U.S. Farm Belt, the balance of power is swinging away from multibillion-dollar agribusinesses.

For over a century, companies such as Cargill Inc. held sway over markets for U.S. corn, soybeans and wheat, quoting prices to farmers who trucked their crops to company grain elevators. Cargill and its peers would then market crops to food and beverage makers across the country.

Now...