Jurors in Maricopa County Superior Court deliberated for only a few hours before deciding that John Allen should get the death penalty.
The jury previously determined that Ame Deal's death was especially cruel or heinous.
Allen, 29, was convicted of first-degree murder and child abuse on Nov. 8.
His 28-year-old wife, Sammantha Allen, was a cousin of Deal's and was convicted of murder in the girl's death in June. She's now the third woman on Arizona's death row.
Prosecutors said the couple forced Ame into the small, plastic box as punishment for stealing ice pops. They went to sleep and the girl was found dead the next morning.
Defense attorney Robert Reinhardt had argued that John Allen, a father of four young children, did not intend for the girl to die and that the other adults in the home created the abusive environment.
But County Attorney Bill Montgomery said Thursday that the Allens "received the only proportionate penalty that could rightly be imposed for the torture and pain they put Ame through. Ame deserved so much more from the adults responsible for her care."
Ame's death was the culmination of a shocking history of abuse at the hands of relatives who were charged with caring for her.
Authorities said the girl was forced to eat dog feces, crush aluminum cans barefoot, consume hot sauce and get in the storage box on other occasions.
She also was kicked in the face, beaten with a wooden paddle and forcibly dunked after being thrown in a cold swimming pool, according to police investigators.
Adults at the home originally claimed Ame hid during a late-night game of hide-and-seek and wasn't found until hours later.
Three other relatives are in prison serving sentences for abusing Ame.
David Deal, who is listed as the girl's father on her birth certificate, is serving a 14-year sentence after pleading guilty to attempted child abuse.
Ame's legal guardian at the time of her death was her aunt, Cynthia Stoltzmann, who is serving a 24-year prison sentence for a child abuse conviction. Ame's grandmother, Judith Deal, is serving 10 years for child abuse.
Authorities said Ame's mother left the family years earlier after suffering abuse from relatives and moved to Kansas without her daughter.