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."
A lodger who worked as a carer for his landlady has been sentenced for killing her in their south-west London flat.