According to the documents, the pleas were part of a deal in which prosecutors agreed to drop the reckless-burning charges, and won't request jail time at sentencing.
The two men each agreed to pay $5,000 in restitution.
McVey sentenced both men on Monday, suspending a six-month jail sentence for each, on condition that they complete one year of probation and pay the entire $5,000 in restitution, plus interest.
The Dump Fire burned 5,507 acres and cost $2.1 million to extinguish.
Charging documents state that Nielsen and Conant were target shooting near Saratoga Springs at 11:30 a.m. on June 21 when an explosive target ignited dry weeds and spread, burning the mountainside, court documents state.
Fire investigators discovered packaging linked to an explosive target the men used during their shooting session. A fingerprint on the packaging was traced to Nielsen, court documents state.
The blaze forced about 2,500 residents to evacuate from nearly 600 homes in Saratoga Springs and Eagle Mountain. It also left the city with a barren hillside, which led to massive debris flows and flooding that damaged several homes in early September.