Authorities apprehended him in the early hours of yesterday, about six hours after deputies were called to a trailer on the Tule Indian Reservation in California, US, on Saturday night.
Inside, they found the bodies of a man and a woman and the body of another man was nearby. Deputies also discovered a wounded boy.
Tribal council secretary Rhoda Hunter said today the woman and two men found dead were Celaya's mother Irene (60), and her two brothers Francisco Moreno (61) and Bernard Franco (53).
She said the wounded boy and the two girls were Celaya's children. The girl who died was identified as Alyssa Celaya. Her five-year-old sister Linea was wounded and the boy, believed to be about seven, is in a critical condition.
Authorities have not said what motivated Celaya to kill his relatives, who lived in a travel trailer on a family compound on the reservation of about 800 people, but tribal members said he had a troubled past.
Shelby Charley, an engineer and supervisor with the Tule River Reservation Fire Department, said of the emergency call: "This is a once in a lifetime kind of deal. It's one of those calls you could go your whole career and not walk into.
"This is one of those calls that will stick with you for the rest of your life."
The winding roads out of the reservation delayed medical help for the boy, Mr Charley said, and thick fog in the area prevented a medical helicopter from responding.
Deputies found Celaya by tracking his mobile phone and pulled him over about 20 miles from the reservation. Celaya opened fire, prompting deputies to respond, sheriff's Sergeant Chris Douglass said.
She did not say how many shots were fired, but said Celaya fired his gun "multiple times". Celaya was shot during the exchange of gunfire, she said.
It was unclear when Celaya shot his daughters.
Police said Celaya was "known to law enforcement and known to use drugs".