O'Riordan was also a member of another band D.A.R.K. and her bandmates posted a tribute to the singer last night.
Irish President Michael D. Higgins said her death was "a big loss" to the Irish arts community and he reflected on his initial introduction to the late vocalist through a Limerick politician.
The couple's D.A.R.K. bandmate, Andy Rourke, added he was "devastated" by her death.
Olé paid tribute to Dolores on the band's official website this week, writing: "My friend, partner and the love of my life is gone". Her family is lovely. "I will continue to stumble around this planet for some time knowing well there's no real place for me here now". I am lost. I miss her so much. "She was an extraordinary talent and we feel very privileged to have been part of her life from 1989 when we started the Cranberries". I will miss her terribly.
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O'Riordan's distinctive Irish lilt and yodel helped fuel the Cranberries' rapid rise in the early 1990s with global hits "Linger", "Dreams" and "Zombie". In a statement to ET, the musician's rep said that she was in London "for a short recording session". Dolores O'Riordan, lead singer of Irish band The Cranberries, has died.
A spokesman said police were continuing inquiries into the death, which was being treated as "unexplained".
"Family members are devastated to hear the breaking news and have requested privacy at this very hard time", the publicist, Lindsey Holmes, said in a statement.
She told London's Metro newspaper a year ago that she had been diagnosed with bipolar disorder, and she spoke to the Irish News about her battles with depression.
O'Riordan and Duran Duran's former tour manager, Don Burton, were married in 1994 and had three children.