The British Broadcasting Corporation says Felicia Boots entered the plea on grounds of diminished responsibility and has been ordered detained at a psychiatric hospital.
The 35-year-old jewelry designer was originally charged with murder in the deaths of her 10-week-old son Mason and his 14-month-old sister Lily at their home in southwest London in May.
The BBC says the murder charges were dropped in light of the plea.
In a statement read in court by her lawyer, Boots said she will be "eternally sorry" for her actions and part of her "will always be missing."
Court had heard Boots suffered from post-partum depression after the births of her children, but appeared to be getting better.
The children were found unconscious by their father, investment banker Jeffrey Boots, when he returned home from work.
The family had moved in to their luxury home in London just a few weeks earlier.
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