"Surgery was performed. After two days in the hospital, I came home to start recovery", he says in the clip. "Prognosis is excellent, and I expect to be back in the studio and taping more 'Jeopardy!' programs very, very soon".
He gave no specific timetable for when he might return. The 77-year-old, who has hosted the show for more than three decades, was suffering from subdural hematoma due to an accident he had in October of 2017.
On Thursday, Deadline reported that Trebek, 77, had been rushed to Cedars-Sinai Medical Center on December 15 after suffering complications from hitting his head in a fall in October.
He also thanked viewers for their concern.
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Trebek was since diagnosed with a subdural hematoma or, as he describes it, "blood clots on the brain".
As the show's episodes are taped months in advance, it's likely that Trebek's leave will not impact production of the show too much.
The College Championship filming will take place in March and air in April.
Trebek has been hosting the Emmy-winning show since Griffin decided in 1984 to revive it as a daily daytime show. The rest of the broadcast schedule will remain uninterrupted, the statement said.