Kelly, 43, checked herself into the facility voluntarily Monday for alcohol problems, and passed away Wednesday night in her sleep.
"I spoke to her on Monday and she was hopeful and confident, looking forward to putting this part of her life behind her," said her agent, Craig Wyckoff.
"She had been fighting demons for a while and finally lost her battle," Wykcoff said.
In 2008, Kelly opened up about her struggles with alcohol. She was arrested several times, including drunk driving in 2010.
"I had lost a baby," Kelly said. "As a result of that I lost it. I lost everything and I was abusing alcohol."
Kelly filed for divorce in June from her estranged husband Robert Gilliam, who was convicted of beating her in May and served 35 days in jail. Her new boyfriend blamed Gilliam for her recent relapse.
She made her first television appearance on "Married... with Children" in 1992 and landed the role of Laurie Forman, Eric Forman (Topher Grace) on "That '70s Show" in 1998.