Ball, 87, was jailed at the Old Bailey in 2015 for sexual offences against 18 young men over three decades.
The self-styled confidant to the Prince of Wales was released from prison in 2017, having served 16 months.
A spokesman for Charles previously said it remained "a matter of deep regret" that he and others were "deceived" by the clergyman.
After his release, Ball went to live with his twin brother Michael Ball in Cornwall before they moved to Langport, Somerset.
An inquest in Taunton heard Ball suffered ill health and depression in the years leading up to his death.
On June 4 this year, he was admitted to Musgrove Park Hospital in Taunton before being discharged on June 12.
He was readmitted the next day following a fall, having sustained fractures to his rib and left clavicle.
Ball was discharged on 20th June but fell while attempting to climb stairs to his bedroom hours later.
He died at Musgrove Park Hospital on the morning of 21st June from respiratory failure and multiple rib fractures.
Tony Williams, senior coroner for Somerset, concluded that Ball's death was accidental.
"Peter Ball suffered a number of falls during which he has sustained multiple rib fractures and gone on to develop a fatal respiratory failure," the coroner said.
"He was a retired bishop. My conclusion will be one of accidental death."
The inquest was not attended by members of Ball's family but a statement from his brother Michael Ball was read.
Ball was bishop of Lewes between 1977 and 1992 and became bishop of Gloucester in 1992.
He went to live with his twin brother, who was bishop of Cornwall from 1990 to 1997, after resigning that post in 1993.
"The shock of all that probably started a downward turn in his health," Mr Ball's statement said.
He said his brother had "for various reasons become depressed at times".
Ball was admitted to hospital twice between 2015 and 2017 for chest and kidney complaints.
"In his final months, he became weaker and weaker with his lungs and his ability to walk or even stand," Mr Ball said.
"He had two spells in hospital before he died and probably should not have come home a second time.
"I think he desperately wanted to die at home.
"On June 20, he tried to get up a small flight of stairs without telling me to his bedroom and after two steps, lost his footing and fell appallingly."
Ball was taken back to hospital at 3am, with staff calling his family at 4.30am to say that he was dying.
His brother described holding Ball's hand until he took his final breath at 7.30am.
"He died gently and peacefully as far as I could see," Mr Ball said.
A post-mortem examination concluded that Ball died from respiratory failure and multiple rib fractures.
It found Ball's lungs and heart contained "significant disease", Mr Williams told the hearing.
A report by the Independent Inquiry into Child Sexual Abuse (IICSA) said Ball was an example of how a senior member of the Anglican church "was able to sexually abuse vulnerable teenagers and young men for decades".
It accused the Church of England of "putting its own reputation above the needs of victims" and offering secrecy and protection for abusers that allowed them to "hide in plain sight".
On the prince's role, the report said: "The actions of the Prince of Wales, in speaking about Ball with the (then) Archbishop of Canterbury (Lord Carey) and a member of Lambeth Palace, and the Duchy of Cornwall buying a property to rent to Ball and his brother, were misguided.
"His actions, and those of his staff, could have been interpreted as expressions of support for Peter Ball and, given the Prince of Wales's future role within the Church of England, had the potential to influence the actions of the Church."
Charles, who will be supreme governor of the Church of England when he becomes king, told the inquiry in a written statement that he "at no stage (sought) to influence the outcome" of any police investigation into Ball.
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