The Irish musician, who was originally from Limerick, led the band to worldwide success in the 1990s with singles including "Linger" and "Zombie", died suddenly, her publicist has confirmed, BBC reported on Monday.
"Of course she was a superstar and an inspiration to so many people, not least from Limerick".
Noel Hogan, Mike Hogan, and Fergal Lawler, O'Riordan's current band mates in The Cranberries, also paid tribute to her on Twitter, calling her an extraordinary talent and saying they feel privileged to have known her since 1989.
President Michael D Higgins said: "It is with great sadness that I have learned of the death of Dolores O'Riordan, musician, singer and song writer". Taoiseach (Irish Prime Minister) Leo Varadkar called her "Limerick's greatest ever rock star", and that her band "captured all of the angst that came with your teenage years".
Dolores O'Riordan was born on September 6th, 1971 in Limerick, Ireland and was the youngest of seven.
Parry explained: "Only yesterday did I discover that her group, or she herself, had composed the song in memory of the event in Warrington".
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The Cranberries released their final album, Something Else, in 2017.
The members of the Cranberries also expressed their grief in a tweet.
Cranberries were set to tour the Europe, the United Kingdom and the USA last spring and summer, but had to cancel numerous dates due to health problem O'Riordan was having.
O'Riordan's trademark powerful, unique voice, with its yodels and Irish accent, came to characterize the band's sound. Last year Chester Bennington, and early this new Year Dolores O'Riordan. Last year The Cranberries cut short a world tour because of the singer's back problems.
"She was very shy, very quiet, hadn't much confidence", she said.
"I was excited to once again be a part of the magic she was able to create", Kovac said.
Ms O'Riordan was pronounced dead at the scene.
O'Riordan liked the metal band's version and offered to add some of her own vocals to it.
They were seen a year ago on nights out in Ireland smiling and holding hands after they first performed together in 2009.