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Kasem's daughter, Kerri, shared the news Sunday in a Facebook posting.
According to a statement from Kasem's PR, the disc jockey passed away at 3:23 a.m.
For the past two weeks, Kasem was hospitalized at St. Anthony's Hospital in Gig Harbor, Washington following a family feud between Kasem's wife, Jean, and three children from his first marriage.
According to Kasem's children, Kasem suffered from Lewy body disease, a form of dementia.
For more than four decades, Kasem lent his voice talents to the radio hosting music countdown shows.
His most popular show, "American Top 40," has been around since 1970. Ryan Seacrest took over hosting duties in 2004.
Kasem also provided the voice for Shaggy in the "Scooby-Doo, Where Are You!" cartoons.
A memorial service will be held Friday.
In his memory, here's a clip of Kasem opening the "American Top 40" in 1970: