A statement from his publicist said the entertainer had been diagnosed with "an incurable brain tumour", and thanked well-wishers for their support.
Middlesbrough-born Daniels, whose career has spanned nearly four decades, found fame in the 1980s with his BBC TV series The Paul Daniels Magic Show.
His wife, Debbie McGee, tweeted: "With great sadness."
Mark Linsey, acting director of BBC Television, said: "We're sorry to hear this sad news and our thoughts are with Paul and his family."
Daniels, whose real name is Newton Edward Daniels, developed his magic skills in working men's clubs.
He made his TV debut on talent series Opportunity Knocks in 1970, and came second.
He was then given a regular slot on ITV variety show The Wheeltappers And Shunters Social Club, hosted by the late comedian Bernard Manning.
He made the move to the BBC in 1979 and launched The Paul Daniels Magic Show, which ran for 15 years.
He became one of the biggest stars on British TV, becoming known for a string of catchphrases, including the line: "You'll like this... not a lot, but you'll like it."
He said he had first used the line at a club in Yorkshire as a way of dealing with a heckler.
Daniels and his wife, a fellow performer and his on-stage assistant, married in 1988.
As well as numerous appearances on magic shows, Daniels has presented game shows including Wipeout and Odd One Out.
He appeared as a contestant on the BBC's Strictly Come Dancing in 2010, and was the second person to be voted off in the series.
In a 2014 interview, McGee explained how, having left the Iranian national ballet where she was a soloist, she was initially unenthusiastic about working with a magician.
But she said she was converted after seeing Daniels on quiz show Blankety Blank.
"He was very funny - he took his jacket off and had a Superman T-shirt on and red knickers over his trousers. I was in hysterics.
"He still makes me laugh, all day long, even when I want to be angry," she said.
In recent years, the couple has toured regularly with a magic and comedy show, but a planned appearance at the Leicester Comedy Festival two days ago was cancelled at short notice, as was another date in Nottingham the following night.
Daniels' manager said all his future shows had been cancelled.
A statement said: "We can confirm that one of our greatest magicians and entertainers of all times, Paul Daniels, has sadly been diagnosed with an incurable brain tumour.
"On behalf of Paul, Debbie and their families, we thank you for your kind concerns and support at this sad time and ask that their privacy continues to be respected. There will be no further comments at this time."
Illusionist Dynamo, whose real name is Steven Frayne, wrote on his Instagram account: "Just read this sad news! Sending my love and respect to Paul, Debbie and all the family! #MagicLegend".
A tweet was also published on the official Dick and Dom page of children's entertainment presenters Richard McCourt and Dominic Wood, saying: "Heartbreaking news of my true hero @ThePaulDaniels. You inspired and encouraged me to do the job I still do today. Sending strength and love."
Magician and entertainer Paul Daniels, 77, has been diagnosed with terminal cancer, his family has said.