Lauren Dickason, 42, previously admitted to killing her two-year-old twin daughters Maya and Karla, and their six-year-old sister Liane at their home in the town of Timaru in the South Island nearly two years ago.

The qualified medical professional denied murder, arguing she was mentally disturbed and didn't know what she was doing at the time.

Dickason tried to kill her children using zip ties before she suffocated them with pillows.

She then placed them in their beds under the covers and tried to kill herself.

During a four-week trial, prosecutors pointed to worrying messages and online search history made by Dickason that included comments about wanting to kill her children and Google searches for "most effective overdose in kids".

The defence portrayed Dickason as a loving mother who spiralled into post-partum depression and was in such a dark place that she had no choice but to kill her children, the New Zealand Herald reported.

"In her mind, she was killing them out of love - she was killing herself and she didn't want to leave the children... she was so sure this was the right thing to do she persisted," defence lawyer Anne Toohey said.

Dickason faces a sentence of life imprisonment.

Her and husband, Graham Dickason, had moved to New Zealand from South Africa days before the murders, seeking a more stable lifestyle.

Mr Dickason, an orthopaedic surgeon, told police that he knew his wife was struggling with her mental health and motherhood, but had no idea she was capable of killing the children.

Following the trial, a jury rejected the legal defence under the country's insanity and infanticide law under the Crimes Act 1961.

The act states that if a woman causes the death of any child of hers under the age of 10 and at the time of the offence, the "balance of her mind was disturbed", she is only liable to a prison sentence of up to three years, if found guilty.

Dickason appeared motionless in the dock, and cried quietly as she left court following the verdict, Radio New Zealand (RNZ) reported.

Her parents issued a statement, encouraging families and individuals to be "aware of the symptoms of post-partum depression" as they said the deaths of their granddaughters were the result of their daughters' illness, according to RNZ.

Detective Inspector Scott Anderson said police wanted to express their deepest sympathies to family members who would never get to see Liane, Maya, and Karla grow up and live out their lives.