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Bridges used the signature voice of his character The Dude from the 1998 cult-classic film The Big Lebowski to disclose his condition, tweeting: "As the Dude would say.. New S**T has come to light."
The 70-year-old said he is starting treatment for the condition and that the "prognosis is good."
The actor is a seven-time Oscar nominee, winning the award in 2010 for his role as a country musician in Crazy Heart.
A veteran of the industry and from a prominent Hollywood family, Bridges is known for his laid-back personality and has acted in critically acclaimed movies such as Starman, Thunderbolt and Lightfoot, The Fisher King, and the Coen brothers' remake of True Grit.
He has also appeared in commercially successful films like the first instalment of the Marvel franchise Iron Man.
The actor thanked his well-wishers and promised to keep everyone posted on his recovery.