A jury in Chicago has convicted Oscar-winner Jennifer Hudson's former brother-in-law of murdering her mother, brother and seven-year-old nephew in what prosecutors' described as an act of vengeance by a jilted husband.

Hudson, who expressed her undisguised disdain for William Balfour and endured weeks of excruciating evidence about the October 2008 killings, was visibly overcome with emotion as the verdict was read last night.

Her eyes filled with tears and she shook her head and bit her lip. Afterwards she looked over at her sister, Julia Hudson, and smiled.

Balfour, 31, who faces a mandatory life prison sentence, showed no emotion.

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

With no surviving witnesses to the murders or fingerprints, prosecutors built a circumstantial case against Balfour by calling 83 witnesses over 11 days of evidence. Witnesses said he threatened to kill the entire family if Julia Hudson spurned him.

Balfour's lawyers said someone else in the crime-ridden neighbourhood on Chicago's South Side targeted the family because of alleged crack-cocaine dealing by Jennifer Hudson's brother, Jason.

But during the 30 minutes in which they called just two witnesses, they presented no evidence to support that theory.

Public defender Amy Thompson said she would appeal against the verdict.

"It has always been our position and it still is that William Balfour is innocent of these murders," she said.

Cook County state's attorney Anita Alvarez reiterated what prosecutors had told jurors: that the evidence against Balfour was overwhelming.

Jurors said their deliberations were cordial and that Jennifer Hudson's celebrity did not influence them.

The verdict came shortly after jurors sent the judge a note saying they were split, though they did not say they were hopelessly deadlocked.

Jurors said afterwards that it took some of them more time to piece everything together, and that a key was mobile phone records showing Balfour was in the area when the killings happened.

Jennifer Hudson, who was in Florida at the time, attended every day of the two weeks of evidence, sobbing when photos of her relatives' bloodied bodies were displayed to jurors during closing arguments.

Ms Alvarez said Hudson would not speak to the media about the verdict but would release a statement "at the appropriate time".

Hudson, 30, rose to prominence as a 2004 American Idol finalist. But she became a bona fide star for her performance in the film adaptation of the musical, Dreamgirls, for which she won the 2007 Academy Award for best supporting actress.

Hudson was the first witness prosecutors called and during her more than 30 minutes on the stand talked about her murdered family members and spoke endearingly about her nephew, Julian King, whom she called Tugga Bear.

She said she knew Balfour since the eighth grade at school and always deeply disliked him.

Balfour had lived in the Hudsons' three-storey Englewood home after marrying Julia Hudson in 2006. He moved out in early 2008 after falling out with his wife, but witnesses told jurors he often stalked the home.

The killings occurred the morning after Julia Hudson's birthday and prosecutors said Balfour became enraged when he stopped at the home and saw a gift of balloons in the house from her new boyfriend.

After his estranged wife left for her job as a bus driver on the morning of October 24 2008, prosecutors said Balfour went back inside the home with a .45-calibre handgun and shot Hudson's mother, Darnell Donerson, 57, in the back, then shot Jason Hudson, 29, twice in the head as he lay in bed.

Prosecutors said Balfour then drove off in Jason Hudson's sport utility vehicle with Julian - Julia's son, whom she called Juice Box - and shot the boy several times in the head as he lay behind a front seat. His body was found in the abandoned vehicle miles away after a three-day search.

The defence tried to counter the portrayal of Balfour as an embittered husband by noting Julia Hudson continued to have sex with him until just days before the killings.

In heated closing arguments on Wednesday, Ms Thompson, almost shouting, said prosecutors had failed to prove their case. Prosecutor James McKay retorted that the defence was exploiting a popular misunderstanding that circumstantial evidence is lesser evidence.

The Hudson sisters left the court without speaking to reporters but released a statement today extending a prayer to the Balfour family, saying "we have all suffered terrible loss in this tragedy".

"It is our prayer that the Lord will forgive Mr Balfour of these heinous acts and bring his heart into repentance some day," they said in the statement, which also thanked prosecutors for their "dedication and tireless work" and praised police and trial witnesses.