An Illinois judge gave William Balfour three life sentences on Tuesday for the 2008 killings. The sentencing came after the judge denied Balfour's request for a new trial.
"You have the heart of an arctic night," Cook County Circuit Judge Charles Burns told Balfour. "Your soul is as barren as dark space."
Hudson, an Oscar-winning actress and singer, was in the courtroom next to her sister for the sentencing, and at one point dabbed her eyes with a tissue.
Balfour was married to Hudson's sister, Julia. Prosecutors contend he shot the family members in a jealous rage because Julia was dating another man.
The only person to give a victim impact statement in court was Gregory King, the father of Hudson's nephew. He told the judge he felt like his heart was ripped out when he found out his son, Julian King, was dead.
"I miss picking Julian up from the school bus," King said. "I miss going on field trips with him ... I miss him spending the night with me and my other children."
The Associated Press contributed to this report.