William Balfour, the estranged husband of Hudson's sister Julia, was convicted in May of killing his in-laws in October 2008 and then hiding his stepson's body to try to cover up his crimes.
"Your soul is as barren as dark space," Judge Charles Burns told Balfour as he imposed the maximum sentence possible. "You have the heart of an arctic night."
State law requires a mandatory minimum of life in prison with no chance of parole for those convicted of multiple murders.
Burns said that in the interest of justice, the three life sentences should be served consecutively, and he also imposed a further 120 years for charges of kidnapping, home invasion and possession of a stolen vehicle.
Balfour, who did not testify or show any emotion at trial, made a brief statement prior to the sentencing in which he offered his "condolences to the family" and proclaimed his innocence.
"My deepest prayer goes out to Julian King," he said of his seven-year-old stepson. "I loved him and I still love him."
Hudson, who did not testify at the sentencing hearing, shook her head in disgust at his statement. Another woman rushed out of the courtroom, quietly sobbing and muttering, "I hate him."
The only victim impact statement came from Julian's father, who spoke of his pain and rage at the loss of his son.
"It was like a chunk of my heart was ripped out," Gregory King told the court. "I will never understand William Balfour's senseless, horrific acts."
Burns lashed out at Balfour for daring to proclaim his love for a boy who he said had likely looked up to him until the moment his stepfather shot him in the head.
"The fact that you tell us in open court that you love that child is an insult to all of us," Burns said, his voice thick with emotion. "I don't think you have one ounce of remorse in your soul."
Prosecutors said Balfour acted out of an obsessive jealousy when he shot his way into Hudson's childhood home and killed everyone inside after getting into an argument with his estranged wife.
Julia Hudson was at work at the time of the shooting and came home to find her mother, Darnell Donerson, 57, dead on the floor in her nightgown.
She was so distressed that she ran outside to call police and did not realize immediately that her brother, Jason Hudson, 29, was dead in his bed or that her son was gone without a trace.
The boy, Julian King, was eventually found hidden under a shower curtain on the floor of his uncle's stolen sport utility vehicle, which had been parked across town.
Crime scene photos shown at trial showed his lifeless little arm stretched out across the back seat.
The murders on Chicago's South Side upended Hudson's life less than two years after the one-time "American Idol" contestant collected a best supporting actress Oscar for her role in "Dreamgirls."
Hudson, who released her second studio album "I Remember Me" in March 2011, and sang "I Will Always Love You" in memory of the late Whitney Houston at this year's Grammy awards, attended the entire trial.
She was accompanied by her longtime partner, professional wrestler David Otunga, her sister, other relatives and security guards.
Mindful of her wish for privacy and the massive media presence, the court allowed Hudson and her family to use a private entrance to the building so they could escape the ever-present cameras. (AFP)
