The singer, best-known for her chart-topping power ballad Total Eclipse of the Heart, died unexpectedly in a hospital in Portugal where she was being treated for an illness, her family said.
Tyler was hospitalised in May in Faro, where she had a home, for emergency intestinal surgery.
She had been placed in an induced coma for a period but was reportedly improving last month.
Chicago star Zeta-Jones said her "heart is broken" after hearing that the singer died on Wednesday night while Sir Cliff, who sang a duet with her on the song Taking Control, grieved the loss of his "wonderful friend" in a Facebook post.
Zeta-Jones, 56, said Tyler was a big part of her life after marrying her cousin, Robert Sullivan, and shared a photograph of the pair together on Instagram which was taken the night before her wedding.
"An extraordinary woman with vocals to match. A one of kind artist, who so easily could have been a comedian because she was one of the funniest people I ever met," Zeta-Jones said.
"Thank you Bonnie for the joy you brought so many. Sleep tight beautiful lady. We shall forever 'Keep A Welcome In The Hillsides' of Wales for you. Sending my love to Robert and the family."
Sir Cliff added: "Bonnie's infectious zest for life entertained so many around the world, and to be a good friend to all, including me.
"It is shocking news to wake up to this morning and I send my love to her family at this very sad time."
Sir Rod Stewart said in a post on Instagram: "We shared similar styles of vocalising. She was a good pal, a true soul stirrer. I sing It's A Heartache every night on tour. I'll miss you darling Bonnie."
Meanwhile, Doctor Who showrunner Davies praised the "fabulous" singer who he "loved" since he was a teenager.
In a post shared on Instagram, he said: "I never met her, though I must've lived a mile or so from her house - and that house was the stuff of legend. She was adored."
He added: "I think it's quite a Welsh thing to lose your accent when you leave home. But NOT BONNIE!
"My God, that magnificent Skewen rasp never buckled, and I think that says a lot about how strong she was. What a gorgeous girl. Night, cariad (darling). Thank you for the music."
Liz Mitchell, the original lead singer of Boney M, said: "She burst onto the scene at exactly the same time as Boney M in the second half of the 1970s, and our paths crossed often, in TV studios and theatres across Europe.
"We became very good friends, and regularly met up for dinner over the following decades. She was a lovely person with a fantastic voice, and I'll miss her very much."
Welsh broadcaster Carol Vorderman remembered the "extraordinary" singer, whose real name was Gaynor Hopkins, in a video on Instagram and said she was regarded as a legend, particularly amongst women.
Vorderman said: "It's difficult to explain if you don't live in Wales that Bonnie represented something to us, and she will be very, very sorely missed."
Rocker Bryan Adams, known for hits such as (Everything I Do) I Do It For You, remembered "dear Bonnie Tyler" in a post on X.
He wrote: "She had such a great voice and I'll always be grateful of her beautiful version of Straight From The Heart. Thanks Bonnie. RIP."
Tyler represented the United Kingdom in the 2013 Eurovision Song Contest with the song Believe In Me.
with PA
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