The author, known for her provocative social commentary, was described as an “inspiration” who “changed the art of writing” online.
She died from complications from Parkinson’s disease, according to her publisher Penguin Random House, which announced her death on Thursday.
English musician Marr wrote: “RIP Joan Didion. A singular genius and inspiration.
“For anyone who is interested see the Netflix doc ‘The Centre Will Not Hold’. Class.”
The official account of The Doors tweeted a quote by Didion, which went: “‘On the whole my attention was only minimally engaged by the preoccupations of rock-and-roll bands, but The Doors were different, The Doors interested me.
“The Doors’ music insisted that love was sex and sex was death…’”
“R.I.P. Joan Didion, 1934-2021,” the account added.
Other celebrities shared personal stories online of Didion and encounters with her and her work.
Comedian Rob Delaney said he has the “deepest gratitude” to the writer, who had helped him through a “brutal, dark time”.
“When my son was getting chemo for the cancer that would ultimately kill him, a very close friend of mine died by suicide,” he said.
“Shortly afterward I read The Year of Magical Thinking & was thrilled, electrified that someone else had gone through 2 nightmares at once & written about it.
“Deepest gratitude to Joan Didion for how she helped me during a brutal, dark time.”
Rosanne Cash, daughter of American musician Johnny Cash, said: “I was honored to meet her once, at a dinner party shortly after The Year of Magical Thinking.
“We were lucky to have her for 87 years.”
Oscar winning-actress Reese Witherspoon said: “A brilliant author who changed the art of writing.
“Thank you #JoanDidion for sharing your stories and work with the world. My prayers go out to all who knew and loved her.”
Fellow US actress Jessica Chastain said: “Seizing the moment & celebrating Joan Didion today.”