Neville Hord, who stabbed supermarket worker Jodie Willsher to death in an Aldi store in Skipton, North Yorkshire, has been jailed at Bradford Crown Court for at least 30 years.
Hord admitted stabbing her to death at the store where she worked, pleading guilty to murder.
The 44-year-old had been accused of stabbing Jodie, 30, while she was on duty at the supermarket in Skipton on December 21 last year.
He will serve a minimum term of 30 years before being considered for parole.
Jodie was married with a young child and her family were well-known in the town.
Prosecutor Peter Moulson QC told the court how Hord stabbed mother-of-one Ms Willsher several times in the store before he was stopped and restrained by members of the public.
He said it was a "cold-blooded public execution perpetrated for the purpose of revenge".
The prosecutor said the attack was witnessed by many people, including a child as well as caught on CCTV.
Mr Moulson said Hord was the ex-partner of Ms Willsher's mother, Nicole Dinsdale, and his motive was "revenge".
He said the attack was pre-planned and the defendant also took an axe with him to the supermarket.
Mr Moulson said Hord told police: "Jodie made things very difficult in my and her mother's relationship."
He said the defendant admitted putting a tracking device on Ms Willsher's car and had been planning the killing for two weeks, buying a pistol crossbow as an "option weapon".
The prosecutor said Hord admitted he went to the store to kill Jodie and told officers he thought she had smiled at him as they made eye contact in the supermarket before he stabbed her.
He said the defendant admitted taking the axe into the store as "back up, just in case".
In a statement read to the court, Ms Willsher's husband Malcolm, said his life and that of his daughter Megan had been ripped apart.
He said mother and daughter had an "unbreakable bond".
Mr Willsher said his daughter has told him: "I hate you daddy for not bringing mummy back."
He described how his daughter had been looking forward to opening her Christmas presents with her mother and the family had a trip to Disneyland planned on Boxing Day.
Mr Willsher said: "I'm so scared he'll get out and do something to Megan."
Judge Jonathan Durham Hall QC told Hord he was "truly and horribly rotten to the core".
He said: "You sentenced her, in your mind, to death."
The judge said: "You chose a time and a place to, in effect, execute; to kill; to murder."
He said the killing was calculated to cause the "maximum pain, horror, shock and trauma".