Patrick Nogueira, 21, fled to his native Brazil shortly after the killing at the family's home in the village of Pioz near central Guadalajara in August 2016.
He returned to Spain in October 2016 and turned himself in to police after the corpses of the family were found in plastic bags at their home.
Nogueira's uncle and aunt, both from Paraiba state in Brazil's northeast, had been dismembered.
The defence argued that Nogueira suffered a “mental disorder” and hoped his confession would mitigate the sentence.
Marcos Campos Nogueira and his wife Janaina Santos Americo were killed alongside their two young sons. Photo: Facebook
The jury found that Nogueira had “intentionally killed” the four victims.
“He knew what was good and bad, and the consequences. It wasn't an erratic act, it was planned and he knew the consequences,” the jury concluded.
Nogueira will be sentenced at a later date. He is expected to receive a life sentence of at least 25 years.
On the opening day of his trial, Nogueira said he was not able to control his emotions.
“I have noticed that my emotions, the way I behave, the way I react, is not the same as others, it is always aggravated,” he said.
“If I could control it, it would be wonderful, not only for me but for others. I would have liked it if none of this happened… I did not chose to function the way I function,” he added.