The teenager initially feigned ignorance regarding the death of his parents and a younger sibling.
But mounting evidence against the 19-year-old made him confess to the heinous crime, Bangkok newspaper The Nation reported.
The incident happened at Pathum Thani, a province in Thailand, on Sunday.
Earlier, the suspect had tried to pin the crime on to his younger brother, who also among the dead.
The suspect told the police that his brother had poor academic records and that when he was berated by his parents, he became angry and killed them.
But Police Colonel Sunthorn Himarat said they started having doubts about this claim after records showed the younger boy was a good student.
He said: "We then examined the older boy's academic records and found the suspect had study-related problems himself. From there, we found so many pieces of evidence against him."
When investigators inspected the crime scene, they found further evidence that the teenager had fabricated the story, Bangkok Post reported.
They found that the 9mm pistol used in the crime was dropped near the right hand of the 16-year-old, but all three victims were shot in the left side of the head.
The younger brother was right-handed, so it would have been difficult for him to shoot himself on the left side of head.