Felix Gutierrez-Cortez, 34, strangled Anna Maria Thomas, 61, in her Wandsworth home in December 2013.
He told authorities she had fallen unconscious while meditating, but was found guilty of manslaughter by diminished responsibility.
At the Old Bailey he was given an indeterminate sentence in a secure facility under the Mental Health Act.
The court heard Ms Thomas had given him a place to stay in exchange for Gutierrez-Cortez acting as her carer.
On 10 December the defendant called 999 claiming he had found his landlady dead and her body was found in a bedroom covered in a duvet.
He later changed his story to say she regularly became unconscious during meditation and that he had stayed in the lounge for two days while she meditated in the spare bedroom.
A post-mortem examination revealed she had been strangled days before Gutierrez-Cortez contacted emergency services.
Det Insp Andy Rees said: "Our investigations demonstrated that she was a caring mother and grandmother and a deeply religious woman with a wide circle of friends who will miss her deeply."

Broad Oak Toiletries Ltd, based in Tiverton, manufactured toiletries and health and beauty products, employing 214 staff.
A spokesperson said the company had ceased to trade immediately after a deal fell through to sell the business.
Capacity issues at its Tiverton plant were also blamed.
One employee, who asked to remain anonymous, said: "I am so scared for the future now. We haven't been paid for January and are worried any new buyer will take it on without honouring the debts."
In a statement the company said: "Regrettably it has been necessary to effect the redundancies of all employees."
Administrators said: "The company exhausted all possible options to continue to trade and, ultimately, in the absence of a buyer of the business as a going concern, it was forced to cease to trade and unfortunately all employees have been made redundant."
A lodger who worked as a carer for his landlady has been sentenced for killing her in their south-west London flat.
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More than 200 people have lost their jobs after a Devon toiletries company confirmed it has closed.