William Balfour is charged with three counts of first-degree murder for the 2008 shootings of Hudson's mother, brother and 7-year-old nephew. He was found guilty of all counts Friday.
Prosecutors said Balfour shot the three family members in an act of vengeance against Hudson's sister, Julia Hudson, to whom he was married but estranged at the time.
Jurors reached a verdict after deliberating for three days. Balfour faces a mandatory sentence of life in prison.
Prosecutors say Balfour shot Hudson's mother, Darnell Donerson, 57, in the living room of the Hudson family home on Chicago's South Side on Oct. 24, 2008, then shot Hudson's 29-year-old brother, Jason Hudson, in the head as he lay in bed.
Balfour then allegedly abducted Julia Hudson's son, Julian King, and shot him as he lay behind a front seat of an SUV. His body was found in the abandoned vehicle miles away after a three-day search.
Prosecutors presented 11 days of testimony and called 83 witnesses, starting with Jennifer Hudson. With no surviving witnesses to present, prosecutors spent two weeks laying out a largely circumstantial case against Balfour, a 30-year-old one-time gang member.
Hudson attended every session of the trial and was present when the verdict was read Friday.
The Associated Press contributed to this report.