Grace, 22, vanished while on a round-the-world trip as she visited New Zealand – disappearing just before her birthday from the Citylife Hotel, Auckland.
Kempson was living at the same hotel where she was last seen alive.
He was met with chants of “scumbag” from the public gallery as he appeared wearing a blue prison jumpsuit at Auckland District Court.
The 26-year-old is charged with murdering the backpacker, from Essex, between December 1 and 2.
It has also emerged the two had contact before the killing, with him saying to her “beautiful, very radiant” in a comment on Facebook.
Her body was discovered over the weekend near a beauty spot on the outskirts of Auckland – and a post mortem was carried out today, cops confirmed.
“All of us hope justice for Grace is fair, swift and ultimately brings you some peace”
Judge Evangelos Thomas
Judge Evangelos Thomas told members of the Millane family, who were in court: “Your grief must be desperate.
“All of us hope justice for Grace is fair, swift and ultimately brings you some peace.”
New Zealand’s prime minister Jacinda Ardern gave an emotional apology to the family of Grace, saying: “Your daughter should have been safe here, and she wasn’t, and I’m sorry for that.”
Speaking to reporters about the death, Ms Ardern said: “I cannot imagine the grief of her family and what they would be experiencing and feeling right now.”
The last confirmed sighting of Ms Millane was at 9.41pm on December 1, the day before her birthday, at the Citylife Hotel, when she was seen with a “male companion”.
Since arriving in New Zealand from Peru on November 20, she had been in near-daily contact with her family.
Police received a missing person report on Wednesday and began a major search and public campaign that saw dozens of calls made to a helpline.
Ms Millane’s father, David Millane, flew to Auckland and made a public appeal for help finding his daughter, who he described as “lovely, outgoing, fun-loving (and) family-orientated”.
Details have begun to emerge about his personal life following his arrest, with him reportedly estranged from his family after his parents separated.
New Zealand media organisation Stuff reported that his grandfather had helped raise him and was struggling to come to terms with the allegations.
It has not yet been revealed how the pair met or the possible motive for the alleged murder.
Kempson’s paternal grandmother told the news website he had spent time living in Australia.
Detectives said they had identified a “location of interest” after the investigation led them to a spot on Scenic Drive, a country road about 12 miles west of the city centre, on Saturday night.
Speaking at the scene on Sunday afternoon, Det Insp Beard said investigators had “located a body which we believe to be Grace” about 10 metres from the roadside.
Two large blue and white tents had been erected and investigators wearing white overalls were seen nearby.
Scenic Drive snakes through dense rainforest in the Waitakere Ranges, which lie to the west of Auckland.
The spot where police found the body is in the vicinity of the Waitakere Reservoir and dam, a beauty spot with hiking trails.
Police said Toyota Corolla hatchback was hired from a central Auckland rental firm just before lunchtime on December 2, the day after Ms Millane was last seen alive.
It was later found in Taupo, a town around 170 miles from Auckland.
Police have appealed for sightings of the car in the west Auckland area between 6.30am and 9.30am on Monday.
Her brother, Declan Millane, paid tribute by sharing pictures on social media of him and his sister, adding the lyrics of You Are My Sunshine.
He wrote on Instagram: “You are my sunshine, my only sunshine. You make me happy when skies are gray. You’ll never know, dear, how much I love you. Please don’t take my sunshine away.”