The pair had met on dating site Tinder.
Ms Millane, who was from Wickford in Essex, had travelled to New Zealand after graduating from the University of Lincoln.
She had previously visited numerous places in Chile and Peru, following the footsteps of her mother's own travels as a young woman.
Speaking via video link to the court, Ms Millane's mother, Gillian, spoke of how her daughter's "tragic life was cut short by your willful, cruel actions," as she addressed her daughter's murderer.
She said: "You took it upon yourself to murder my beautiful Grace.
"That innocent young lady.
"On a daily basis I torment myself over what you did."
In a powerful victim impact statement, Ms Millane addressed her daughter's killer directly: "She died terrified and alone in a room with you," she told the 28-year-old, putting emphasis on the final word of her statement.
Giving his testimony, Grace's older brother, Declan, spoke of his family being "ripped apart" when his sibling stopped responding to messages sent on her 22nd birthday - the day she is thought to have been murdered on.
He said: "The following weeks were the hardest and worst weeks of my life.
"I remember taking the phone call from my dad, telling me that Grace's body had been found and I just remember I was instantly sick.
"Ever since December 2018, I cannot close my eyes without reliving that moment of not knowing what happened to my sister - and the thought of how scared she must have been and that I could have done nothing to help her."
Watch Rob Setchell's report here:
What happened to Grace Millane?
On November 30, 2018 Ms Millane matched on the dating app with the man who would take her life.
The following evening she met him for a date shortly before 6pm.
After drinks, the pair heading to her killer's apartment in Auckland's CityLife building and Ms Millane was killed either that night or in the early hours of the next morning - the date of her 22nd birthday.
After her death, her killer did not call police but instead made numerous internet searches for pornography and items to help him dispose of Ms Millane's body.
The following day, her murderer went on another date, again with a woman he met on Tinder, before disposing of Ms Millane's body in a suitcase in a shallow grave off a rural road outside the city limits.
Two days later, a missing person's report was launched by Ms Millane's family.
Police announced a murder investigation had been opened on December 10, 2018.
The man pleaded not guilty when he first appeared in court in the first weeks of 2019.
The defence had claimed the death was accidental and occurred during rough sexual intercourse.
Some 11 months later a jury found he was responsible for the death of the graduate.
Parents welcomed verdict as they spoke outside court house on day of conviction in November 2019
The parent's of Ms Millane sat through the entire trial and in November, on the day her murderer was convicted, they spoke of how they welcomed the verdict.
Her father said: "The verdict of murder today will be welcomed by every member of the Millane family and friends of Grace.
"It will not reduce the pain and suffering we have had to endure over the past year.
"Grace was taken in the most brutal fashion a year ago and our lives have been ripped apart.
"Grace was our sunshine and she will be missed forever. She did not deserve to be murdered in such a barbaric way during her gap year."