One half of the famous culinary duo passed away on Saturday in Edinburgh's Royal Infirmary, her agents said.
"Loved dearly by her friends and many fans all over the world, Clarissa was utterly non-PC and fought for what she believed in, always, with no thought to her own personal cost," read a statement from her agents.
"Her fun and laughter, extraordinary learning and intelligence, will be missed always, by so many of us."
Celebrities and fans took a moment to pay tribute to the chef on social media site Twitter. "Very saddened to hear about Clarissa Dickson Wright. She was always entertaining to watch and was of course a passionate foodie x" tweeted Jamie Oliver.
The broadcaster and food writer shot to fame with her late on-screen partner Jennifer Paterson, who died at the age of 71 in 1999 after being diagnosed with cancer.
The pair travelled the UK on a Triumph Thunderbird motorbike and sidecar for the BBC series, which enjoyed worldwide success and ran between 1996 and 1999.
Clarissa initially began her career as a barrister – she was the youngest woman ever to be called to the Bar up until last year – which was brought to "an abrupt end" by her battle with alcohol.
She was teamed with Jennifer Paterson for the hit show in the 90s by producer Patricia Llewellyn after she discovered her working in an Edinburgh cookery bookshop.
The producer decided to introduce her to who would become her "other half" on TV, Jennifer, who had never before had a cookery lesson.
Clarissa's upcoming 67th birthday on 24 June would have marked her 27th anniversary of no drinking, a birthday her agent said "meant much more to her than another year on the clock".
The famous chef recently said: "I've had a fantastic life and I've done everything I could have wanted to do and more".