Pennsylvania State Police and the FBI arrested the 28-year-old suspect in the Scranton area in the early hours of Friday morning and found the Hyundai at the scene.
Moscow police chief James Fry confirmed at a Friday press conference in Idaho that the Hyundai Elantra had been found, although said they were still searching for the murder weapon.
“We are still looking for all pieces of evidence, we are still looking for the weapon and I can say that we have found an Elantra,” he told the press conference in Moscow.
Authorities narrowed the focus of their investigation to Mr Kohberger after tracing him as the owner of the Hyundai Elantra seen near the crime scene, according to CNN.
When investigators found that he had left the area, the suspect was tracked for four days by an FBI surveillance team from the agency’s Philadelphia office, a source told the news network.
And he remained under surveillance until officials in Idaho could obtain an arrest warrant, at which point law enforcement moved in and captured him.
Investigators previously had ruled out any connection to a white Hyundai vehicle that had been found in Eugene, Oregon, as they sifted through thousands of tips about the cars.
Mr Kohberger is a PHD criminology student at Washington State University, which is around 10 miles from the scene of the crime.
He is the first person to be arrested in connection with the murders and is being held at the Monroe County Prison in Pennsylvania pending his extradition to Idaho, which a judge ordered on Friday.
The bodies of Madison Mogen, Kaylee Goncalves, Xana Kernodle and Ethan Chapin were found at their rental house opposite the University of Idaho in the city of Moscow on 13 November.
The families of the victims had grown increasingly frustrated with the lack of progress in the case, while investigators insisted the trail had not grown cold.
The Moscow Police Department says it had more than 13,000 tips in the case as well as thousands of digital media submissions to comb through.