CHICAGO — The former brother-in-law of Oscar winner Jennifer Hudson was convicted Friday of murdering Hudson’s mother, brother and 7-year-old nephew in what prosecutors described as an act of vengeance by a jilted husband.

Hudson, 30, who openly expressed disdain for William Balfour when she took the witness stand and who endured weeks of excruciating testimony about the October 2008 killings, was overcome with emotion as the verdict was read.

Hudson’s eyes filled with tears and she shook her head and bit her lip.

Balfour, who faces a mandatory life prison sentence, showed no emotion.

Jurors deliberated for three days before reaching their verdict against Balfour, 31, a former gang member who was the estranged husband of Hudson’s sister Julia at the time of the triple murders.

With no surviving witnesses to the Oct. 24, 2008, slayings or fingerprints, prosecutors built a circumstantial case against Balfour by calling 83 witnesses over 11 days of testimony.

Witnesses said he threatened to kill the entire family if Julia Hudson spurned him.