Mrs Fox, a retired nurse known as Judy, was killed between June 12 and 14 last year.
Her remains were eventually discovered in woodland next to the River Severn, off The Lloyds at Coalport near Ironbridge, the following month after an extensive police search.
Lucy Fox, 39 and of Bernard’s Hill, Bridgnorth, had also set fire to a doormat at the Apley Park home occupied by her brother and his family, intending to harm him.
A makeshift device consisting of two aerosol cans wrapped in tape with Fox’s palm and fingerprints were recovered from the grounds in the hours of June 14.
The jury at Stafford Crown Court unanimously determined that she committed the offences of murder and arson with intent to endanger life.
However the jury was only required to determine whether or not she committed the acts, and was not required to bring in verdicts of guilty due to the unusual nature of the case.
Judge Kristina Montgomery told the court that Fox would be made subject to an hospital order to protect the public.
She said the defendant, who was tried in her absence, had a paranoid illness "consistent with a finding of paranoid schizophrenia".
Fox had given no pleas and was tried in her absence after the court found she was unfit to stand trial and was “not fit to participate in the trial in any meaningful way” due to her mental health.
"It may be that in future a trial to assess her full criminal culpability could take place," the judge said, adding that unless such a trial took place it was important "the public is protected from Lucy Fox".
Judge Montgomery praised members of the Fox family who have been in attendance throughout the trial for their dignity, and said she would read their victim impact statements with sympathy and in private.
"I have no doubt and can only imagine the devastation wreaked on her family and how awful it must be for them to sit through the trial and hear the the details of what happened to Mrs Fox.
"I pay tribute to them," the judge said.
She also praised the jury for its service in the case which she described as "harrowing case for everybody".
Mrs Fox was a company nurse at the Shropshire Star and Express & Star for 13 years, and had been employed at a care home until shortly before her disappearance.
Detective Chief Inspector Mark Bellamy, the senior investigating officer for West Mercia Police, said: “This was a tragic and senseless killing that has left a family absolutely devastated by the loss of their mother, sister and grandmother in truly horrific circumstances and my thoughts remain with them at this incredibly difficult time.
“This was a challenging and complex investigation and I’d like to thank the investigation team for their hard work and commitment that has meant the jury has reached the verdict it has today.”