Regina Edwards, 52, strangled Priscilla Edwards, 78, with a scarf in February, the Old Bailey heard.
Edwards, who lived in Plumstead, south London, had a history of mental health problems. In 1995 she was convicted of stabbing one of her daughters in the leg.
She has been sentenced to life with a minimum of 10 years.
During a phone call to a family member soon after her mother's body was found at her house in Kirkham Street, Plumstead, Edwards said: "I did it, it was me."
Priscilla, a former midwife, was suffering from dementia at the time of her death.
After her 1995 conviction, Edwards - who has a diagnosis of schizoaffective disorder - spent ten years in a psychiatric unit under the care of Oxleas Mental Health Trust.
She was discharged in 2006.
Judge John Bevan, who said there was a "serious risk" she would attack someone again, ordered Edwards be returned to a secure hospital.
If she is deemed suitable for release from psychiatric care within 10 years, she will be kept in jail until eligible for parole.
In statements, Edwards's family said they felt "hurt and extremely angry" and pleaded for her to stay locked up.
They expressed anger at the acceptance of her plea of diminished responsibility, but felt it was inevitable.
Judge Bevan said: "The daughters argue the defendant should be in secure accommodation indefinitely and express considerable concern about the Bracton Centre, where she is at the moment, because they live in the area and in the past she absconded and visited the home.
"There is real fear for their security when she is not taking her medication."

Luke, 18, is one of 14 successful candidates from the 282 youngsters who entered the Fighting Chance scheme.
GB Taekwondo chief Gary Hall said that, like his sister Jade, the teenager is "a good character".
Hall added: "He hasn't got the tactical game finesse his sister has but he has a lot of the basic ingredients."
The 14 who made the cut will undergo a three-month training regime before fighting at the Austrian Open in June.
Performance director Hall added: "This group is really strong. We have done [the Fighting Chance scheme] four times and this has got to be one of the strongest intakes we have had.
"They will go on a three-month programme, including participation in the Austrian Open, to see how they perform.
"If they are really making progress in the system then we will continue with them."
Find out how to get into taekwondo in our special guide.
A woman who strangled her mother because she thought she was a "witch" has pleaded guilty to manslaughter.
[NEXT_CONCEPT]
The brother of Wales' double Olympic taekwondo champion Jade Jones has been signed up by the sport's Great Britain academy.