The 'Big Lebowski' star just announced his cancer diagnosis on Twitter, telling fans ... "As the Dude would say.. New S**T has come to light. I have been diagnosed with Lymphoma."

Jeff is keeping a positive attitude despite the seriousness of the disease, adding ... "I feel fortunate that I have a great team of doctors and the prognosis is good."

Jeff's already undergoing treatment ... he doesn't specify which kind of cancer treatment, but promises to keep his fans updated on his recovery.

Tons of folks, including lots of celebs, are already reaching out to Jeff ... and he says he's "profoundly grateful for the love and support from my family and friends."

The Oscar-winning actor also says he's thankful for everyone's prayers and well-wishes and he ended his announcement with a message to remember to go vote.