The British-born singer died "peacefully" at her ranch in southern California on Monday morning, surrounded by family and friends, her widower confirmed.
Leading the tributes from the entertainment world was John Travolta, who starred opposite Newton-John in the hit 1978 film Grease.
Writing on Instagram, Travolta said her "impact was incredible" and signed off his tribute as "your Danny".
"My dearest Olivia, you made all of our lives so much better," he wrote.
"Your impact was incredible. I love you so much. We will see you down the road and we will all be together again.
"Yours from the first moment I saw you and forever! Your Danny, your John!"
Dionne Warwick, who recorded a duet with Newton-John in 2006, tweeted: "Another angelic voice has been added to the Heavenly Choir.
"Not only was Olivia a dear friend, but one of the nicest people I had the pleasure of recording and performing with. I will most definitely miss her.
"She now Rests in the Arms of the Heavenly Father."
Oscar-winning actress Marlee Matlin recalled starring alongside Newton-John in the 1996 film It's My Party, one of the first films to address the topic of Aids patients dying with dignity.
She said on Twitter: "I am SO saddened at the news of the passing of Olivia Newton John.
"I remember being so star struck when I met her at my first Hollywood gathering for Paramount.
"She was the sweetest and brightest light and I loved getting to know her on It's My Party. RIP dear, sweet Olivia."
American filmmaker and actor James Gunn called her his "first real crush" and revealed he previously bought her home in Malibu.
"Really sad to hear about the passing of Olivia Newton-John," he tweeted.
"My first real crush as a kid.
"I loved Grease & her music & I coincidentally also bought & lived in for a while the wonderful home she built in Malibu. May she Rest In Peace."
Filmmaker Edgar Wright, whose credits include Last Night in Soho and Baby Driver, added: "Olivia Newton John so completely dominated the charts and Top Of The Pops when I was a kid, it felt like she was pop music.
"And yes, Xanadu is still a stone cold classic song. RIP."
Kiss co-founder and frontman Paul Stanley said in a brief tribute: "So very sad. She was everyone's sweetheart."
Actress Gabrielle Union described the impact on her of Newton-John's performance in Grease.
"Grease is my #1 movie of all time and made me a lifelong Olivia Newton John fan," she said.
"Me and my sister watched Xanadu more times than I could count.
"Sending so much love and prayers to a real gift of a woman and talent."
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