The 71-year-old broadcaster revealed he recently received the diagnosis and is receiving “excellent treatment”.
The University Challenge host added that his symptoms are “currently mild”.
In a statement to the PA news agency, Jeremy said: “I can confirm I have recently been diagnosed with Parkinson’s disease. I am receiving excellent treatment and my symptoms are currently mild.
“I plan to continue broadcasting and writing for as long as they’ll have me and have written about my diagnosis in more detail for the June issue of the marvellous Saga Magazine.
“I will not be making any further comment.”
Jeremy is perhaps best known as the former host of BBC Two’s Newsnight.
He presented the flagship current affairs programme from 1989 to 2014, during which time he interviewed high-profile figures from politics and culture.
He has also fronted University Challenge since 1994, making him the longest serving current quizmaster on UK TV.