Irish Prime Minister Leo Varadkar tweeted: “Her music was loved around the world and her talent was unmatched and beyond compare.”
Singer Alison Moyet tweeted she had a “voice that cracked stone”, while ex-Stone Roses star Ian Brown said working with her was “a highlight of my musical life”.
Bryan Adams posted a picture of O’Connor and said he “loved” working with her.
Irish UFC star Conor McGregor also shared images and said Ireland had “lost an iconic voice and one of our absolute finest”.
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The singer was known for her outspoken views on subjects such as religion, war and feminism.
She infamously tore up a photo of the Pope on Saturday Night Live in 1992 to protest against abuse in the Catholic Church.
O’Connor converted to Islam in 2018 and changed her name to Shuhada Sadaqat, but still performed under her old name.
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O’Connor referenced his death in an emotional tweet last week in which she said she was “lost” without him.
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She posted a row of crying emojis alongside a photo of the pair and said she had been “living as undead night creature since [his death]”
“He was the love of my life, the lamp of my soul. We were one soul in two halves,” she wrote.
The singer recorded 10 studio albums and was nominated for eight Grammys, but never topped the huge success of Nothing Compares 2 U – originally written by Prince.
The intense close-up of the singer – and her tear during the video – is instantly recognisable to a generation of fans.
She once said she had shaved her head in response to music bosses pressuring her to be conventionally glamorous.
Sinead O’Connor was ridiculed – but time proved her right
Sinead O’Connor was speaking truth to power long before speaking truth to power was a thing.
In 1990, when she shot to global stardom with her mesmerising version of Nothing Compares 2 U, the Catholic Church still held sway in Ireland.
“Catholic Ireland” was a place where contraception, divorce, homosexual activity and abortion had all been illegal.
For a woman to shave her head and raise it above the parapet to challenge the powerful institutions of church and state was unthinkable.
Who could forget her tearing a picture of Pope John Paul II in half during an appearance on Saturday Night Live in America?
She was ridiculed in the wake of it and faced calls for her music to be banned but her decision to stage a protest against clerical abuse proved prophetic.
Struggling with her own mental health, it was easy for the powerful to write her off as a loose cannon, but time proved her right and justified her brave stance.
In a statement expressing his condolences, Ireland’s president Michael D Higgins spoke of the “authenticity” of her music and that brutal honesty sums up her life.
She spent most of it openly searching for peace and her legion of fans across the world will hope she has now found it.
O’Connor began playing on the streets of Dublin using a guitar given to her by a nun and released debut album The Lion and the Cobra in 1987.
Her last record, I’m Not Bossy, I’m The Boss, came out in 2014.
“Everyone wants a pop star, see?” she wrote in her memoir two years ago. “But I am a protest singer. I just had stuff to get off my chest. I had no desire for fame.”
She was married four times – the final one ending after 16 days in 2011 – and had four children.