The statement was posted on Facebook.
He was reportedly found on an Indian Reservation in Kitsap County.
A judge on Monday had ordered an investigation into the whereabouts of the famed radio countdown host, 82, as it emerged he had been removed from Los Angeles without his children's knowledge.
He has advanced Parkinson's and can no longer speak.
Kasem has been in various medical facilities chosen by his wife, Jean Kasem, and Kasem's kids have long been battling over their father.
Casey Kasem gained fame with his radio music countdown shows,American Top 40 and Casey's Top 40, and was the voice of Shaggy in the cartoon Scooby-Doo.