Police discovered the bodies of the children and 29-year-old woman inside the Jack Cooper Drive house around 1.30pm on Monday.
The Sydney Morning Herald has identified the victims as Adeline Yvette Rigney-Wilson and her children.
A 30-year-old man was arrested outside the home and taken to hospital under police guard.
He was charged overnight and is expected to face Elizabeth Magistrates court later today.
Chief Inspector Alby Quinn told reporters at the scene the incident appeared to be domestic violence-related, according to the Sydney Morning Herald.
"This matter doesn't involve any other people and it does appear at this stage to be domestic related," he said.