When he asked them to bring their puppies and they refused, he disappeared from the window for a few minutes.
"[He] returned with a 12-gauge shotgun and BB gun," said the judge's sentencing statement, published by WATE TV.
"[He] then announced to the girls that he had guns.
"The victim then laughed at [the boy] and stated that she believed they were not real.
"[He] then made certain the gun was loaded, cocked the hammer of the gun, and shot the victim just above the heart at a downward trajectory from a distance of three to five feet from inside the window."
The girl fell backwards and quickly lost consciousness. She died shortly afterwards in her mother's arms.
The judge noted that boy had been trained in firearm safety and had hunted with his father and grandfather, but offered no first aid in the aftermath of the shooting.
Rob Johnson, a spokesman for Tennessee's department of children's services, said officials were still trying to determine where he should be held.
"Like any other child who comes into custody, he would need a thorough assessment and evaluation to determine the best placement," he said.
"At this time, it would likely be at an intensive treatment program at one of our private providers."
The shotgun was legally owned by the boy's father.
His sentencing comes weeks after Barack Obama announced plans to tighten gun controls across the US.