The British-born, Melbourne-raised performer died in her sleep at her home in California, according to husband John Easterling in news shared on Tuesday. She was 73.
"Thank you Livvy. Thank you for your deep heart, your playfulness, your constant encouragement and positivity," niece and Aussie actress Tottie Goldsmith posted on Instagram.
"You were more than an auntie to us and you were a gift to this world."
Goldsmith revealed on Tuesday night that the family will accept the offer of a state funeral.
Dame Olivia, best known for her role alongside John Travolta in the smash movie musical Grease, endured a recurring battle with breast cancer.
The global star was remembered as a friend, a great talent and an inspiration to fellow performers.
Travolta was among the first to pay tribute to his former co-star.
"My dearest Olivia, you made all of our lives so much better. Your impact was incredible. I love you so much," he posted on Instagram.
The impact of Dame Olivia's passing also hit hard in Australia on Tuesday.
Prime Minister Anthony Albanese remembered her as an inspiration to many.
"The work she did though her cancer research centre was important and inspirational," he tweeted.
"Her legacy will live on, in her music, her films and her determination that one day we will find a cure for cancer."
Kylie Minogue, whose career path followed that of Dame Olivia with her elevation to international fame from humble beginnings in Melbourne, said on Twitter: "Since I was 10-years-old, I have loved and looked up to Olivia Newton-John. And, I always will.
"She was, and always will be, an inspiration to me in so many, many ways."
Hollywood actor Hugh Jackman described Dame Olivia as his "first crush".
"Not only was she one of the most talented people I've known … she was one of the most open hearted, generous and funny. She was a one-of-a-kind spirit," he wrote on Instagram.
"I kissed her (poster) every night before bed. Her legacy will only grow stronger in the years to come. A fighter for healing from cancer that knows no bounds. I love you Olivia."
Singer Delta Goodrem, who played Dame Olivia in a 2018 biopic, wrote on Instagram that the star was both a mentor and friend.
"The whole world will feel this heartbreak today because the entire world felt Olivia's unmatched light," she said.
"I don't have all the words I would like to say today, but I hope everyone will join in celebrating our beloved Olivia, her heart, soul, talent, courage, grace ... I love you forever."
Music guru Molly Meldrum said Dame Olivia's passion for life was unwavering.
"Tonight, the stars will shine a little brighter and I am heartbroken," he said.
Victorian Premier Daniel Andrews said the Grease star's generosity saved lives and her advocacy spanning many years provided hope for others.
"She took her cancer journey and used that to save lives and change lives, and that's just a deeply impressive thing," he said.
Austin Health, home of Melbourne's Olivia Newton-John Cancer Research Centre, said in a statement it was an especially sad day for everyone involved in the facility.
"Olivia was a driving force to win over cancer, for treating the whole person and looking after their mind, spirit and body. Having the opportunity to meet Olivia was a joy, her kindness and light was irrepressible," a spokesman said.
"The ONJ Centre was her dream, and we are proud of everything we achieved together. We will continue our work to honour her legacy."
The centre is planning a memorial service as the government works with family on a possible state funeral.
Dame Olivia was admitted to the Australian Recording Industry Association Hall of Fame in 2002 and made a Companion of the Order of Australia in 2019.
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