Davis County sheriff's detectives told reporters they took the 15-year-old into custody Wednesday night, hours after the two victims were found dead in their West Point, Utah, home, The Salt Lake Tribune reported.
Sheriff Todd Richardson said the cause of death for both victims was consistent with "penetrating knife wounds" and investigators are treating the case as a homicide.
Police found the victims after their mother called 911 to report she had found the 4-year-old son dead, and the 15-year-old and 10-year-old missing. Investigators said the mother had left the 15-year-old in charge of his siblings while she took her other children to a dance recital Wednesday afternoon.
Police found the 15-year-old at about 11:30 p.m. in Layton, about 5 miles from his home. He was evaluated at a hospital and then booked on suspicion of homicide.
"We believe he acted alone," Richardson said.
Davis County Sheriff's Sgt. Susan Poulsen said the boys' father is in the military and has been away on active duty. No other information about the family has been released.