William Balfour, who was married to Hudson's sister Julia, was found guilty in May of three counts of first-degree murder, as well as aggravated kidnapping, home invasion, residential burglary and possession of a stolen vehicle in the shooting deaths of members of the Hudson sisters' family.
Prosecutors argued Balfour, now 31, shot his victims to death in 2008 in a jealous rage because Julia had left him and was dating someone new.
Judge Charles Burns first denied Balfour's motion for a new trial, then sentenced him to three consecutive life terms in prison for his crimes, the Chicago Sun-Times reported.
Balfour, who did not testify at his trial, expressed remorse, particularly for killing Julia's 7-year-old son, Julian, before he was sentenced.
"My deepest sympathies to Julian King. I loved him. I still love him," the Sun-Times quoted Balfour as saying as he also offered "condolences and prayers" to Hudson's family.