KABC-TV reports, last month Aguirre was found guilty of first-degree murder in the death of his girlfriend's 8-year-old son, Gabriel Fernandez.
The jury found him guilty of first-degree murder and also guilty in the special circumstance allegation of murder involving the infliction of torture.
Jurors then had a choice between recommending life in prison or the death penalty.
Deliberations in the penalty phase began Monday and jurors gave notice they had reached a recommendation by Wednesday afternoon.
The official sentencing by the judge is scheduled for March.
One juror told KABC that the group was divided when they headed into deliberations Wednesday morning. It took a lot of debate and deliberation to reach their unanimous decision, she said.
"It's just really sad," the juror said. "It's a heartbreaking story. You just never think something like that can even happen. The things I heard - it's just unimaginable."
During trial, prosecutors presented a long history of abuse against the boy committed by Aguirre and allegedly by the boy's mother, Pearl Fernandez.
That included shooting him with a BB gun, feeding him cat feces and forcing him to sleep while gagged and bound inside a small cabinet.
Gabriel died in May 2013.
Pearl Fernandez is to be tried separately.
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