In joint statement following Tuesday night’s West End performance of the show, they said it was a “huge honour to follow in Olivia’s footsteps each night” and that they had all be inspired by her work.
Dame Olivia’s death was announced on Monday on social media by her widower John Easterling, who said she had died peacefully at her home in California, following a battle with cancer.
The actress was best known for playing Sandy in the 1978 film opposite John Travolta, who played Danny Zuko.
As the show concluded, actress Olivia Moore, who plays Sandy in current run, addressed audiences against the backdrop of a large image of Dame Olivia, set within the neon pink staging.
“Ladies and gentlemen, I am sure you have all heard the incredibly sad news that Olivia Newton-John passed away yesterday evening,” she said.
“She of course played Sandy in the film and she is an icon who has inspired countless young performers across the world, especially all of us in this company.
“It is a huge honour to follow in Olivia’s footsteps each night and perform those songs that she made world-famous with millions of fans that continue to celebrate her incredible talent.
“We are dedicating our run of Grease to Olivia’s memory and all that she stood for and tonight.”
Ms Moore, 26, added that a collection for breast cancer support, a charity for which Dame Olivia raised much awareness, was being held at the exits of the theatre.
High-profile figures from across the creative industries have paid tribute to the singer and actress, including Abba, Dolly Parton, Kylie Minogue, Peter Andre, as well as Travolta, who led tributes on Monday.
Dame Olivia came fourth at the Eurovision Song Contest 1974 in Brighton, where Swedish pop outfit Abba triumphed with Waterloo, launching their careers.
The global superstars described her as the “nicest, kindest and most loving woman” and hailed her “brave fight” against an “invincible enemy” following her death.
Anni-Frid Lyngstad and Agnetha Faltskog, who performed alongside Bjorn Ulvaeus and Benny Andersson in the group, paid tribute in statements to the PA news agency.
Lyngstad, known as Frida, said: “What do you feel, what do you say when the nicest, kindest and most loving woman leaves us to travel somewhere else?
“The heart aches to know Olivia’s brave fight against an, in her case, invincible enemy.
“That she never gave up or complained about her situation, but instead told us her story so that we would understand and want to help others affected.
“I am grateful to have known a person like you, Olivia, and you will always be in my heart. With love, your friend Frida.”
Faltskog added: “So sad to hear of Olivia’s passing … A fine person has left us – and there are many of us who mourn her now.
“My thoughts go out to the family, and her music and personality will always remain in memory.”
Sir Cliff Richard, who shared a close friendship with Dame Olivia and performed with her many times, wrote on Facebook: “I’m just one of an army of lucky people who knew and loved her. How could we not love her? She was gorgeous, gifted and had a heart of Gold. Also, a bunch of records that were Gold, but her Golden Heart is her legacy to us.
“When she was first diagnosed with cancer Livvy put her career on hold for years. Why? Because she wanted to inspire other sufferers to do as she did… fight the ugly disease, although she said in one interview that she wasn’t in a battle with cancer just that she had something that she simply wanted to get rid of!”
The singer said he would miss her before adding: “Let’s all keep her alive in our hearts and memories.”
US country legend Parton said she was “so happy that our lives crossed paths” in her own tribute to Dame Olivia.
Travolta paid tribute on Instagram shortly after news of Dame Olivia’s death was announced on Monday evening.
“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!”
Aside from her hit role in Grease, Dame Olivia was also a multi-platinum selling artist, with two singles and two albums having earned the certification from the Recording Industry Association of America (RIAA).
She is survived by her husband as well as her daughter Chloe Lattanzi.