The Irish singer, from Kilmallock, Co Limerick, was pronounced dead aged 46 on January 15 at the Hilton Hotel in Park Lane where she had been staying while recording.
Coroner Shirley Radcliffe told an inquest at Westminster Coroner’s Court that the cause of death was drowning due to alcohol intoxication and concluded that the death was an accident.
Pc Natalie Smart, who attended the scene, told the inquest: “I saw Mrs O’Riordan submerged in the bath with her nose and mouth fully under the water.”
The inquest heard that there were empty bottles in the room - five miniature bottles and a bottle of champagne - as well as containers of prescription drugs with a quantity of tablets in each container.
Toxiclocology tests showed only “therapeutic” amounts of medication in O’Riordan’s blood, but showed up 330mg of alcohol per 100mls of blood - meaning she was more than four times the 80mg legal limit for driving.
The coroner said it would seem that O’Riordan - who was wearing a long-sleeved vest and pyjama bottoms - became unconscious in the bath, adding: “There’s no evidence that this was anything other than an accident.”
The inquest, which was attended by O’Riordan’s mother, brother and sister-in-law, heard that the singer checked into the hotel on January 14.
She was in touch with room service at around midnight and phoned her mother at around 3am.
She was later found unresponsive in the bathroom and confirmed dead at 9.16am.
The inquest heard that O’Riordan had bipolar disorder but responded well to treatment.
The hearing was also told that she went through periods of abstention and periods of excessive drinking.
The inquest heard that he had spoken to psychiatrist Dr Seamus O Ceallaigh on January 9 and was in “good spirits”.
O’Riordan, who would have turned 47 on Thursday, the day of the inquest, was renowned for her distinctive singing voice.
In a statement issued after the hearing, the band said: “On January 15th 2018 we lost our dear friend and band mate Dolores O’Riordan.
“Today we continue to struggle to come to terms with what happened.
“Our heartfelt condolences go out to Dolores’ children and her family and our thoughts are with them today.
“Dolores will live on eternally in her music. To see how much of a positive impact she had on people’s lives has been a source of great comfort to us.
“We’d like to say thank you to all of our fans for the outpouring of messages and their continued support during this very difficult time.
“We request, please, for our privacy to be respected at this time.”
The band enjoyed huge success in the 1990s with tracks including Zombie and Linger.
O’Riordan - who was also a member of alternative rock group DARK - had been working on a new studio album with The Cranberries in the months before her death.
The mother-of-three had been in London to record a cover of Zombie with hard rock band Bad Wolves when she died.
Sales and streams of The Cranberries’ back catalogue rocketed by 1,000% in the days after her death.
In 2014, O’Riordan split from her husband of 20 years, former Duran Duran tour manager Don Burton.