Fletcher was last seen on surveillance footage Friday morning, where she appeared to be forced into a vehicle, according to a police affidavit.
Cleotha Abston, 38, was arrested Saturday and charged with especially aggravated kidnapping and tampering with evidence. After Fletcher's body was identified, Abston was also charged with first-degree murder and first-degree murder in perpetration of kidnapping, police said.
At a news conference Tuesday, Memphis Police Chief Cerelyn Davis said Fletcher's remains were found "in the rear of a vacant duplex apartment." It is "too early to say" where and how Fletcher died, she added.
While the investigation is ongoing, Memphis District Attorney Steve Mulroy said authorities have "no reason to think this is anything other than an isolated attack by a stranger."
"To lose someone so young and so vital is a tragedy in and of itself," Mulroy said. "But to have it happen in this way with a senseless act of violence is unimaginable."
Fletcher went jogging at around 4 a.m. Friday, the affidavit states. At about 7 a.m., when she had not returned home, her husband reported her missing. A civilian found her cellphone and a pair of Champion slides on a street in the area. He turned the items over to Fletcher's family, who gave them to investigators.
Surveillance footage of the incident "showed a black GMC Terrain passing and then waiting for the victim to run by," according to the affidavit. A man then exited the car, "ran aggressively toward the victim, and then force[d] the victim Eliza Fletcher into the passenger's side of the vehicle," during which "there appeared to be a struggle." The car sat in a parking lot for about four minutes before driving away.
DNA found on the sandals was a match for Abston, and surveillance footage also showed him wearing them the day before, police said. Police determined Abston was living at an address for a woman who owns a black GMC Terrain, and cellphone records showed he had been present at the scene of the crime.
A neighbor interviewed by investigators said she saw Abston cleaning the car's interior and "behaving oddly" on Friday morning. His brother, Mario Abston, confirmed this to police, saying he'd seen him "washing his clothes in the sink" and acting very strange," according to the affidavit.
Fletcher was a mother of two and a prekindergarten teacher at St. Mary's Episcopal School in Memphis. Second Presbyterian Church, to which Fletcher's family belongs, previously called for prayers for her safe return. Her grandfather was billionaire Joseph "Joe" Orgill III, the owner of a hardware distribution company, who died in 2018.