Investigators said Jonathan Martin Oliver, 27, told them where he tossed the knife used in the homicide. However, investigators have not yet been able to find it.
Oliver has been charged with first-degree murder, first-degree burglary and robbery with a dangerous weapon.
It happened around 5 a.m. Sunday at 70 Primrose Drive.
Deputies responded to an alarm at that location and found the body of Annie Grace Davis, 78, inside.
Deputies say the motive of the murder appears to be robbery. They said Oliver broke into Davis' home; surveillance cameras caught him roaming around the house dressed in all camouflage.
He was arrested at his parents' home less than a mile away later the same day.
Billy Caulder, Davis' brother, said she was stabbed several times.
He described her as an outgoing person despite dealing with devastating loss in her life.
"She lost her ex husband that she divorced," said Caulder. "Then she remarried and lost him. Lost her two boys. So she's been through a lot in the last few years."
Still, he said, she always made time for her family.
"If I needed anything she was very accommodating to everybody," he said. "That's about all I can tell you."