Col. John Fortunato said Matthew Flugence, 20, told law enforcement officials Wednesday he stabbed Ahlittia North, 6, during the weekend, CNN reported.
Flugence, who sometimes babysat Ahlittia, was arrested Tuesday.
Ahlittia's body was found in a trash can near her mother and stepfather's apartment in Harvey, a New Orleans suburb.
"I don't know what I else I can say about the character of an individual that just admitted to killing a 6-year-old," Sheriff Newell Normand told reporters Wednesday. "I think that speaks for itself."
Flugence had an outstanding warrant charging him with sexual assault on an 11-year-old girl last year, Fortunato said.
Flugence's brother Russell, was arrested earlier on suspicion of obstructing justice in Ahlittia's death, Normand said. Russell Flugence did not reveal information about the crime or information that implicated his brother, the sheriff said.
Matthew Flugence told detectives Wednesday he killed Ahlittia Saturday with a knife investigators recovered during his arrest, Normand said.
Jefferson Parish Coroner Gerald Cvitanovich said the girl had four stab wounds, two each in her neck and abdomen. She also had bruising about her body, he said, but there were no obvious signs of sexual assault.