The jury of eight women and four men delivered a majority verdict, stating that Dickason was not insane at the time of the killings and was guilty of murder.
She faces a life sentence for each killing.
Dickason killed her two-year-old twins and their six-year-old sister in September 2021 at their home in Timaru, a city on the South Island, about a month after the family had migrated from South Africa.
Her husband, Graham, found the three children dead and his wife in a serious condition upon arriving home after a dinner with colleagues.
The prosecution argued that Dickason knew when she killed her daughters that what she was doing was morally wrong and the act was murder.
The judge, Cameron Mander, remanded Dickason to custody in a hospital psychiatric unit until her sentencing.
She had been in hospital since the murders.
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