Prosecutors said Kyle Clifford killed his 25-year-old ex-girlfriend Louise Hunt and her 28-year-old sister Hannah Hunt with a crossbow before stabbing their mother, Carol Hunt, 61, to death on July 9.
Appearing via video link at Cambridge Crown Court, Clifford admitted to three counts of murder, one of false imprisonment and two counts of possession of offensive weapons - the crossbow and a 25cm knife.
He pleaded not guilty to a charge of raping Louise Hunt.
The three women, who are the family of well-known BBC radio racing commentator John Hunt, were found with serious injuries at their home in the quiet residential neighbourhood of Bushey, northeast of the capital.
Police and ambulance crews tried to save the three women but they were pronounced dead at the scene.
Police launched a manhunt for the suspect before he was found injured in a cemetery in Enfield, north London.
Clifford, who served in the military from 2019 for about three years, had shot himself in the chest with the crossbow.
Following the attacks, Home Secretary Yvette Cooper said she was urgently considering whether tougher crossbow laws were needed but no proposals have yet been put forward.
People in the United Kingdom do not need a licence to own a crossbow but it is illegal to carry one in public without a reasonable excuse.
The weapon has been used in several high-profile crimes in recent years.
In December 2021 a would-be assailant carrying a loaded crossbow broke into Windsor Castle seeking to kill Queen Elizabeth II.
Jaswant Singh Chail pleaded guilty to a treason charge and was sentenced last year to nine years in prison.
