Ayoola Ajayi was charged with aggravated murder, aggravated kidnapping, obstructing justice and desecration of a body, the Salt Lake County District Attorney's Office said at a news conference.
Ajayi, 31, was arrested June 28, more than a week after Lueck disappeared upon returning to Utah from a trip to Southern California for her grandmother's funeral. Her body was found last week in Logan Canyon in Logan, Utah.
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District Attorney Sim Gill said Wednesday that the remains had been burned and were found in a shallow grave in a wooded area. Lueck's arms were bound behind her back with zip ties and she also suffered blunt force trauma to her skull, which a medical examiner said could have been fatal.
Human bone, muscular tissue, a charred cellphone and other personal items were also discovered in Ajayi's backyard, according to Gill. Neighbors had previously told authorities that Ajayi had burned something with gasoline in his backyard around June 17 or 18.
A search of Ajayi's vehicle turned up a gasoline can, Gill said Wednesday.
Investigators do not have a motive and have not revealed how Ajayi and Lueck, who was a student at the University of Utah, knew each other.
Gill said Lueck's cellphone records showed she had exchanged several text messages with Ajayi. Her phone was "powered off" around 3 a.m. shortly after she arrived at the park and it was never turned back on, he said.
Lueck's and Ajayi's cellphone records placed them at the park at the same time, Gill said.
Lueck's family contacted police June 20 after she missed a midterm exam and failed to show up for a scheduled flight back to Los Angeles.
Minyvonne Burke is a breaking news reporter for NBC News.