John Easterling said Dame Olivia was “the most courageous woman I have ever known” and that her caring nature “almost eclipses what is humanly possible”.
The singer and actress, best known for playing Sandy in the 1978 hit film Grease opposite John Travolta, died on Monday aged 73.
She is to receive a state memorial service in Australia.
Dame Olivia was born in Cambridge, England, before moving with her family to Melbourne, Victoria’s capital city, from the age of five.
Daniel Andrews, the premier of the state of Victoria, shared the news on Twitter, writing: “I’m so pleased that Olivia Newtown John’s family have accepted our offer of a State Memorial Service.
“We’re working with Olivia’s family on the details, but it will be more of a concert than a funeral – fitting for a Victorian who lived such a rich and generous life.”
Sharing news of her death on social media, Mr Easterling said she had passed away “peacefully”, surrounded by family and friends.
In a new post, shared from Dame Olivia’s account on Wednesday, he thanked fans for “the ocean of support that has come our way.”
“Our love for each other transcends our understanding,” he captioned a picture of himself and his late wife.
“Every day we expressed our gratitude for this love that could be so deep, so real, so natural. We never had to ‘work’ on it.
“We were in awe of this great mystery and accepted the experience of our love as past, present and forever.”
He continued: “At Olivia’s deepest essence she was a healer using her mediums of song, of words, of touch.
“She was the most courageous woman I’ve ever known.
“Her bandwidth for genuinely caring for people, for nature and all creatures almost eclipses what is humanely possible.
“It is only the grace of God that has allowed me to share the depth and passion of her being for so long.
“In her most difficult times she always had the spirit, the humour, and the will power to move things into the light.
“Even now as her soul soars, the pain and holes in my heart are healed with the joy of her love and the light that shines forward.”
Dame Olivia’s daughter Chloe Lattanzi also posted a tribute and accompanying video to her mother, describing her as “an angel on earth”.
“You are my lighthouse mama, my safe place, my heart space,” she wrote on Instagram.
“It has been my honour and continues to be my honour to be your baby and best friend.”
Australian Prime Minister Anthony Albanese also paid tribute to Dame Olivia after her death, writing on Twitter: “Olivia Newton-John was a star. A bright, joyful glow in our lives.
“From the moment we saw her, she was a warm, enduring presence and her voice became a big part of the Australian soundtrack.
“Above all she was a wonderful, generous person.”
Aside from her hit role in Grease, Dame Olivia was also a multi-platinum selling artist, with two singles and two albums having earned certification from the Recording Industry Association of America (RIAA).
She is survived by her husband and daughter Lattanzi.