Manager Craig Wyckoff says Kelly died on Wednesday at a Los Angeles addiction treatment facility she had entered early this week.
No official cause of death was disclosed.
Kelly portrayed Laurie Forman, sister of Topher Grace's lead character Eric, on the Fox series. It concluded in 2006.
Unlike some of her co-stars - Grace, Ashton Kutcher and Laura Prepon - Kelly fell out of the spotlight after appearing on the sitcom until she started making headlines for personal troubles.
She was arrested in November along with husband Robert Joseph Gilliam in connection with a disturbance at their home in North Carolina.
In June, she was arrested on suspicion of drunken driving after her car stalled in California.
TMZ has further details about her death - watch here:
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Quickie time again!
A quick chat!
'I've grown so much'
Chatting about Strictly!
We chat to the lads!
Talking about life!
We sit down and talk!
Chatting in a cab!
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