Julian Stevenson killed his children - Mathew, 10, and Carla, five - apparently in a fit of rage over a custody battle with his French ex-wife.
He had fled on a pair of roller skates but was found moments later, walking in the street and covered in blood.
The unemployed father had confessed to the gruesome crime "but did not go into details of the motive", prosecutors said after his arrest in May.
"He hanged himself on Monday in a sports hall reserved for inmates held in solitary confinement," a source at the local public prosecutor's office told AFP.
Britain's Foreign and Commonwealth Office (FCO) later confirmed the reports to The Local.
"We are aware of the death of a British national in detention in France on 30 December 2013 and we are providing consular assistance to the family,” said a spokeswoman for the FCO.
The murder had shocked the local community in suburban Lyon.
CCTV footage of Stevenson hours before the tragedy shows him buying his children sweets, his son and daughter clutching pink balloons.
The 48-year-old is believed to have had a history of drinking. Stevenson's visitation rights were curtailed after a violent clash with his ex-wife in 2010.
"In 2010, there was an incident of violence with his spouse which led to restrictions on his visitation rights," a source close to the investigation told AFP at the time of his arrest.
Stevenson had visitation rights but only in the presence of another person, the official said, adding that it was the first time he had brought the children home to his apartment on the second floor of a four-storey building without a third party being present.
At the time a neighbour Ahmed Benguedda told AFP the couple had divorced "two or three years ago" and that the man had drinking problems and was a wife beater.
After the divorce the wife, who worked as an assistant accountant, moved out of the apartment they had jointly bought and was living in the Isere region of eastern France.
But the children were "well-balanced", said Benguedda, whose seven-year-old daughter often played with them..