The musician was in London for a recording session when she died suddenly.
A statement said: “Irish and international singer Dolores O’Riordan has died suddenly in London today.
“She was 46 years old.
“The lead singer with the Irish band The Cranberries, was in London for a short recording session. No further details are available at this time.
“Family members are devastated to hear the breaking news and have requested privacy at this very difficult time.”
The singer, from Limerick, enjoyed success with The Cranberries in the 1990s with hit singles including Linger and Zombie.
One of the band’s biggest gigs was supporting US supergroup REM at Murrayfield in July 1995. They also performed on a number of occasions at the Edinburgh Festival Theatre.
In May 2017, The Cranberries cancelled a string of shows after O’Riordan was instructed by her doctors to stop working for a month for medical reasons associated with a back problem.
A further set of shows in North America, due to take place in September and October, was cancelled in July.
On 20 December, O’Riordan tweeted from the band’s official account, writing: “Hi All, Dolores here. Feeling good! I did my first bit of gigging in months at the weekend, performed a few songs at the Billboard annual staff holiday party in New York with the house band.
“Really enjoyed it! Happy Christmas to all our fans!! Xo”
In February 2016, O’Riordan said she would use “music, dancing and performing to improve her mental health” after avoiding a criminal conviction for assault at an airport.
She was ordered to pay 6,000 euros to charity for headbutting, kicking, hitting and spitting on police officers following an alleged air rage incident.
The singer had previously admitted three assaults and obstructing a garda after being taken off an Aer Lingus flight from New York’s JFK to Ireland on 10 November, 2014.
Medical reports produced for the trial at Ennis District Court revealed she had been suffering from mania, mental illness and severely impaired judgment at the time of the incident, and that she remembered nothing about it.
O’Riordan was mother to son Taylor and daughters Molly and Dakota.
President of Ireland Michael D Higgins led tributes to the singer, saying: “It is with great sadness that I have learned of the death of Dolores O’Riordan, musician, singer and songwriter.
“Dolores O’Riordan and The Cranberries had an immense influence on rock and pop music in Ireland and internationally.
“I recall with fondness the late Limerick TD Jim Kemmy’s introduction of her and The Cranberries to me, and the pride he and so many others took in their successes.
“To all those who follow and support Irish music, Irish musicians and the performing arts her death will be a big loss.”
Irish band Kodaline also offered condolences, writing on Twitter: “Absolutely shocked to hear about the passing of Dolores O’Riordan!
“@The_Cranberries gave us our first big support when we toured with them around France years ago! Thoughts are with her family and friends.”
O’Riordan split from her husband of 20 years, the former tour manager of Duran Duran, Don Burton, in 2014.
Duran Duran wrote on Twitter: “We are crushed to hear the news about the passing of Dolores O’Riordan. Our thoughts go out to her family at this terrible time.”
O’Riordan, from Friarstown, Kilmallock, Co Limerick, was renowned for her distinctive singing voice.
She became a multi award-winning musician after becoming lead singer of the band when she was just 18 and went on to sell tens of millions of records.