William Balfour was convicted Friday of the 2008 murders of Hudson's mother, brother and 7-year-old nephew.
He faces a maximum sentence of life in prison.
Balfour, who was married to Hudson's sister Julia, was found guilty 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 the Hudson sisters' family.
Prosecutors argued Balfour shot his victims to death in a jealous rage because Julia had left him and was dating someone new.
"We have many people to thank but our first thank you is to God, always," E! News quoted the Hudson sisters as saying in a statement after the verdict was announced.
"We are so grateful to prosecutors James McKay, Jennifer Bagby and Veryl Gambino and State's Attorney Anita Alvarez and her team for their dedication and tireless work from the beginning. We have the best police department, and they have been with us every step of the way. We thank all of the State's witnesses who came forward on our behalf. We have felt the love and support from people all over the world and we're very grateful."
The sisters also said they are praying for Balfour's family.
"We have all suffered terrible loss in this tragedy," they said. "It is our prayer that the Lord will forgive Mr. Balfour of these heinous acts and bring his heart into repentance someday."