The now 31-year-old William Balfour shot Hudson's mother and brother in their Chicago home in the autumn of 2008. He then kidnapped her 7-year-old nephew Julian King, who was later found dead in a burning vehicle.
Balfour, who had threatened to kill the family for over a month before the incident, was acting in retaliation to Hudson's sister Julia Hudson, who had separated from him after an abusive marriage.
An Illinois jury found Balfour guilty of three counts of first-degree murder on Friday (May 11). He now faces a life sentence in prison and is making plans to appeal the decision.
Hudson broke down in tears during the trial hearing and was later comforted by fiance David Otunga.
WENN reports that the Dreamgirls star has released a statement in conjunction with her sister Julia through attorney Anita Alvarez.
Alvarez told reporters on behalf of the Hudson sisters: "They are both very pleased and very appreciative of the co-operation that we have provided for them. They are relieved and we hope that this verdict gives them some sense of justice."