A statement by the actor and singer's family said: "David died surrounded by those he loved, with joy in his heart and free from the pain that had gripped him for so long.
"Thank you for the abundance and support you have shown him these many years."
Cassidy was rushed to a hospital in Florida last week, with his publicist saying at the weekend that he was suffering organ failure.
He revealed earlier this year he was battling dementia after video emerged of him performing erratically in California.
Cassidy forgot the words to some of his own songs and yelled at a fan to turn off a light that he claimed was blinding him.
He later told People magazine he had been in "denial" about his illness and he had decided to stop touring, saying he wanted to "enjoy life".
Cassidy shot to fame in the early 1970s as Keith Partridge in TV sitcom The Partridge Family, starring opposite his stepmother Shirley Jones.
He went on to enjoy a hugely successful pop career and scored two UK number ones with How Can I Be Sure and Daydreamer.
The magnitude and speed of Cassidy's fame was noted by Rolling Stone in a 1972 article.
It wrote: "In two years, David Cassidy has swept hurricane-like into the pre-pubescent lives of millions of American girls.
"Leaving: six and a half million long-playing albums and singles; 44 television programmes; David Cassidy lunch boxes; David Cassidy bubble gum; David Cassidy colouring books and David Cassidy pens; not to mention several millions of teen magazines, wall stickers, love beads, posters and photo albums."
Cassidy's fame faded after the show ended but he continued to make music and perform concerts for decades.
In recent years he struggled with alcohol problems and was arrested three times for drink-driving between 2010 and 2014.
He was ordered to go to rehab as part of his sentence.
A month after his third arrest, his wife Sue Shifrin-Cassidy filed for divorce.
Cassidy, who has two children, also had to auction off his Florida home in 2015 after filing for bankruptcy.