Theresa Riggi was found dead at Rampton Secure Hospital in Nottinghamshire.
50-year-old Riggi was jailed for 16 years for killing her eight-year-old twins Austin and Luke and her five-year-old daughter Cecilia at their Scotland home in August 2010.
Riggi then tried to cover up the way they died with a gas explosion. She then leaped from the balcony of their second-floor flat in Edinburgh.
The children's bloodstained bodies were discovered lying side by side on the bedroom floor following the explosion. The bodies each carried eight stab wounds.
The murders took place following a marriage split with the children's father; the both of them had been involved in a legal proceeding over the children's custody at the time. Riggi used a separate knife for each of the children.
Riggi was initially charged with murder but admitted three counts of the lesser charge of culpable homicide on the grounds of diminished responsibility.
Lord Bracadale, who judged the case, said at the time "The number and nature of the stab wounds to each child is indicative of a truly disturbing degree of violence which, in order to bring about the deaths of three children, must have been sustained over a significant period of time. It is difficult to envisage the physical commission of such acts."
A court heard that a report into her mental state identified narcissistic, paranoid and hysterical personality disorders. She was sentenced in April 2011 at the High Court in Glasgow.
She was moved from the all-female Cornton Vale Prison, near Stirling, after a string of alleged attacks in 2011.
Rampton Hospital is a high security psychiatric hospital near the village of Woodbeck.
The US-born Riggi was found dead at Rampton Secure Hospital in Nottinghamshire on Monday.
A Nottinghamshire Police spokeswoman said: "We can confirm that we were called to Rampton in the early hours of this morning to the death of a woman. It's not being treated as suspicious and we are preparing a file for the coroner."
Additional reporting by PA