Young was critically wounded after being shot nine times during a vehicle stop at the Poison Spider trail head, outside Moab, on November 19, 2010.
Young managed to return fire but his assailant got away, authorities said. The park ranger survived; he's currently assistant coordinator of Utah's statewide boating program.
The unsuccessful hunt for suspected shooter Lance Leeroy Arellano took investigators from various state agencies to an area of hulking boulders, steep cliffs and winding caves, according to the Grand County Sheriff's Office.
But it wasn't until a pair of real-life Hardy Boys named Caleb Shumway, 23, and his brother, Jarom, 15, took to the rugged terrain that the remains believed to be those of the long sought gunman were discovered, the sheriff's office said.
Shumway was on Christmas break from college, the statement said. He visited the area "for the sole purpose" of finding evidence in the case.
"I almost felt certain I could find them," Shumway said of the remains in an interview with CNN affiliate KSTU
The amateur sleuths at first spotted what appeared to be a human bone and a bag containing a gun and a magazine near the Tangri-La Ranch, the sheriff's statement said.
The remains were in a cave-like area reached by crawling through a narrow entrance to a narrow void in the rocks, the statement said.
Evidence at the scene leads investigators to "believe the remains are those of Lance Leeroy Arellano, the suspect in the shooting of Brody Young," the statement said.
"I've always kind of, here in Moab, wondered if he got away or if he was dead somewhere in the rocks," Shumway told KSTU.
The young man told the station he was prepared to search for weeks.
"The majority of the time that was spent out there was spent in caves, on our elbows and our knees," he said.
The remains were transported to the Utah State Medical Examiner's Office for identification, the sheriff's office said.
"While evidence found with the remains leads investigators to believe they are those of Arellano, we will anxiously continue to wait for confirmation from the Utah State Medical Examiner's Office for positive identification," the Utah Division of Parks department said.
The statement said state parks officials were "grateful for the continued dedication and commitment of our law enforcement partners and volunteers in Grand County."
The brothers discovered bones on the second day of their search, KSTU reported.
"He was way down in the cave," Shumway told the station.
"In fact, the cave he was down in ... there was the initial level of the cave that we crawled into and found the first bone, and then the cave tunnels off to the side, and we found a bag, and then we actually found the actual body. It was over some more, and down even deeper into the ground."
In the bag was a pistol, a magazine and a pair of binoculars, KTSU reported.
"It's really exciting finding some closure for all the families involved, all the police involved, and then just getting to be in the middle of it," Shumway told the station. "It's exciting, and it feels good."