Jay Nava, 27, stabbed Natasha Wake 11 times in the chest and neck at her home in Bournemouth in October.
He then fell asleep beside her body, which he later hid in a cupboard.
A judge at Winchester Crown Court said Nava, from Plymouth, should serve a minimum of 21 years for his "frenzied and violent outburst".
The trial heard the pair had argued while drinking at Miss Wake's home in Harley Gardens on the evening of 1 October.
The dispute may have been provoked by her discovery that Nava had been investigated by the police for an alleged sexual assault on another woman, the jury was told.
Later a child in the house heard a "scream" and came downstairs to find Nava with a knife and Miss Wake lying on the floor covered by a blanket.
He told the girl it was a "game" and sent her to bed.
Nava told the jury he could not remember stabbing Miss Wake, but admitted he scrubbed the walls, wrapped the 26-year-old in a duvet and hid her in a cupboard.
The following morning Nava phoned his mother in Australia and confessed to the killing.
Later that day, police found the former Commando gunner at Hengistbury Head, Dorset, and resuscitated him when he attempted to take his own life as officers approached.
A defence psychiatrist told the jury Nava's ability to control his behaviour was "substantially impaired" by an "underlying narcissistic personality disorder".
In a victim impact statement read to the court, Miss Wake's mother, Shelley Powell, said she was "haunted by Natasha's last few moments".
Ms Powell said: "I knew her fears - that she would not live to see her children grow up."
Passing sentence, Judge Jane Miller QC said Miss Wake's family had seen her go from "infatuated to scared" of Nava because of his "controlling and jealous behaviour".
A former soldier has been jailed for life for murdering his on-off girlfriend while three children slept upstairs.