Felicia Boots, 35, and her husband Jeffrey Boots sobbed in the Old Bailey court in London Monday morning as the woman pleaded guilty to the lesser charges of manslaughter.
The couple's children, 10-week-old Mason and 14-month-old Lily, were found dead last May in their home in Wandsworth, a district of southwest London.
The family was living in Britain as the husband continued his career, most recently with the Royal Bank of Canada.
'I am a good person. I was a good mum'
The Daily Telegraph described the woman as wearing a black suit and white blouse as she told the court, "May 9, 2012 is a day I will be eternally sorry for. It should never have happened and troubles me deeper than anyone will ever know.
"Part of me will always be missing but just know that I am a good person. I was a good mum and I never meant this to happen. I am truly sorry."
The BBC reported that the prosecution dropped murder charges and accepted her plea on the grounds of diminished responsibility.
A preliminary inquest determined both children had been suffocated.
Boots admitted she was suffering from postpartum depression and had abandoned her medication out of fear it would affect her second pregnancy and breast-feeding.
Since her arrest, Boots has been held at a psychiatric unit and the decision to lower the charges to manslaughter were based on the considering of doctor' reports.
The Telegraph reported the woman had tried to take her own life after killing her children.
'A tragic case,' prosecutor says
The BBC reported prosecutor Edward Brown said the Crown had carefully examined medical evidence and spoken with the woman's husband.
"This is a tragic case," Brown told the court, in explaining the Crown's decision to lower the charges.
Presiding over the case, Justice Fulford said, "This is an almost indescribably sad case" but that "what occurred was not as a result of what most people would regard as criminal activity."
"I unreservedly accept that what the defendant did to the two children she and her husband loved and nurtured, was solely the result of psychological and bio-physiological forces that were beyond her control," the judge said.
Boots was ordered to be detained at a psychiatric hospital.