The professional quizzer and comedian posted on Twitter that he "will fight this with every breath I have" before sharing further details of his diagnosis in a blog post, in which he asked to be treated "exactly the same as before".
He said he intends to remain on the ITV quiz show, on which he is known as "The Sinnerman", and to keep writing, performing comedy and quizzing.
He wrote: "Nonetheless my reaction was not one of shock. I spent May this year in New Zealand simultaneously having the comedy month of my life, and worrying about why a right-sided limp was now getting worse.
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"Behind the facade of the cheerful, late-night comedy festival drunk was a man deeply scared about facing the truth when back in the UK."
Sinha said he has had a "really, really tough two weeks", adding: "Cancelling my run at the Edinburgh Fringe, missing the World Quizzing Championships to have brain scans, performing club sets whilst emotionally bewildered, and of course working my way through my loved ones, delivering the bad news.
"With the diagnosis now confirmed, and a treatment plan in place, I now feel far more prepared for the new challenges ahead.
"In the time since my Parkinson's started I have been ludicrously busy, and fully intend to keep Chasing, keep writing and performing comedy, keep quizzing and keep being hopeless at Tasks."
He added: "Dancing On Ice is, I suspect, out of the question."
The NHS describes Parkinson's disease as a condition in which parts of the brain become progressively damaged over many years.
The main symptoms are involuntary shaking of parts of the body, the slowing of movement and stiff, inflexible muscles.
Sinha attended south London public school Dulwich College and later St George's Hospital Medical School in Tooting.
He qualified as a general practitioner in the 1990s but during his time at St George's developed a taste for the stage, honing his stand-up skills in the school's revue.
He has appeared at the Edinburgh Festival Fringe a number of times, with his material drawing heavily on his Bengali background and sexuality.
He has claimed jokingly to be the only gay Anglo-Bengali GP turned stand-up comic.
Sinha's myriad media appearances include BBC Radio 4's The News Quiz, The Now Show and Loose Ends as well as his own programme Paul Sinha's Quiz Culture, and he is currently appearing on Taskmaster on Dave.
He was dubbed "The Sinnerman" after making his debut on The Chase in 2011.
He appears as a quizzer, or a Chaser, on the Bradley Walsh-hosted programme alongside fellow quiz experts Mark "The Beast" Labbett, Anne "The Governess" Hegerty, Shaun "The Dark Destroyer" Wallace and Jenny "The Vixen" Ryan.
Sinha's Parkinson's revelation comes weeks after the BBC's technology correspondent, Rory Cellan-Jones, said he has been diagnosed with the disease.
Steve Ford, chief executive of Parkinson's UK, praised Sinha's decision to speak out about his diagnosis.
Mr Ford said: "Paul Sinha bravely speaking about his Parkinson's diagnosis, and the journey he has been on to get to this point, will do so much to raise awareness of this much misunderstood condition.
"With more than 40 symptoms, Parkinson's undoubtedly throws up new challenges, but with the right treatment and support we can help people to take control of their lives with this unpredictable condition.
"Paul's determination to live well with Parkinson's is mirrored by an incredibly passionate Parkinson's community, determined both to find new and better treatments but also to not let Parkinson's hold them back. We wish Paul all the best with his future projects."