Clarence, who had entered a plea of guilty to manslaughter by reason of diminished responsibility, will be detained until she is declared fit to leave by health professionals.
Alluding to a history of mental illness in her family, Mr Justice Sweeney said that Clarence killed four-year-old Olivia and three-year-old twins Ben and Max during a 'major depressive episode'.
He then issued a hospital order under Section 37 of the Mental Health Act, which gives courts the power to order a compulsory admission to a psychiatric hospital in place of a prison sentence.
Clarence will be eligible to appeal to a tribunal after six months.
Clarence smothered the three children at the family's home in New Malden, London, on Friday, April 18. All three suffered from life-limiting muscle weakening disease SMA Type 2. Her husband, Gary, was in South Africa with the couple's older daughter, who did not have the condition, at the time.
Yesterday, the court heard how a struggling Clarence's mental state had deteriorated further after the family's long-standing social worker was reassigned elsewhere.
Addressing Clarence, Mr Justice Sweeney described how the South African native had 'devoted yourself to providing optimal care for your children, suppressing your feelings of distress and sadness by focusing on their needs'.
"The constant demands placed upon you in the absence of emotional support from others, entirely overwhelmed your psychological resources," he said, adding: "What you did was the product of your mental illness."
Dismissing the option of sentencing the 43-year-old to a prison term, Mr Justice Sweeney ruled that a hospital order was the appropriate response, telling Clarence that she would not be released until she had fully recovered from her mental illness.
Following the verdict, Gary Clarence issued the following statement through his solicitor outside the court:
"The loss of the children's lives at the hands of the mother who cherished them is a tragedy explained by her severe depressive illness. But it is also a tragedy from which lessons need to be learnt.
"Tania's depression was certainly not assisted by the constant pressure placed on the family by some individuals within the medical profession and social services who could not agree with Tania and Gary Clarence's stance of prioritising quality of life for their children and who were not readily willing to submit the children to operations and other interventions they felt were not appropriate in the circumstances.
"Gary Clarence will be making no personal comment until the conclusion of all internal investigations and reviews.
"In due course, he will be assisting Kingston Borough Council in their review of the decisions taken in this case, and he hopes to be able to ensure that never again will a family have to endure the unbearable pressure that eventually overwhelmed the resources of his wife.
"However, he wishes to make it clear that all of the evidence made it plain that the three children were well cared for and loved by their parents and that allegations of "neglect" mentioned in court last Friday were wholly unfounded."
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