The proposal has angered some local residents, one of whom claimed the application was unnecessary and financially driven.
But FCC says the plan is needed to help them restore the tip to the park locals are promised will be built by the end of 2025.
They say most of the soils, which the planning application says may be "hazardous" before being processed, would come from nearby construction sites.
Julie Fourcade, FCC's head of external affairs, said: "The proposed development uses an existing, currently redundant engineered pad, quality assured by the Environment Agency, and would be of a temporary nature.
"The site will in time be infilled and restored as part of the approved landfill restoration scheme by no later than December 31, 2025 and the additional suitable restoration materials are vital to meeting this deadline."
By law, if the company had applied to ferry up 30,000 or more tonnes of soil onto the site, the application would have to be decided by the government.
Setting the bar at 29,999 keeps the decision in the hands of Wakefield Council, the company explained.
Although the planning statement says treating the soil will "possibly include incineration" - a prospect that has also alarmed campaigners - FCC claimed in a statement "there is no proposal for an incinerator attached to this application".
The company says that the process they intend to use will see the soil converted into carbon dioxide and water.
Ms Fourcade added: "Given the levels of built development proposed within West Yorkshire, it is anticipated that the volumes of material required each year would largely originate from the local area.
"The process will be the subject of conditions imposed through an environmental permit, issued and regulated by the Environment Agency.
"Approximately eight HGV loads of soil will be delivered per day on average as part of this application which focuses on restoring the landfill by no later than 31 December 2025 and there is no proposal for an incinerator attached to this application."
Activities at Welbeck have been a source of local controversy for years, with the long-awaited park supposed to have been originally completed by 2008.
A dead whale and human body parts have been among the items dumped at the site.
Local Democracy Reporting Service