The plea agreement includes a sentence of life in prison without parole.
In court, Holbert apologized to Bordeaux's family "for all the pain and horror."
"There isn't anything I can say or do to relieve the pain," he said.
After the apology, Bordeaux's mother Johnna Henson spoke and got frustrated when Holbert wasn't looking at her.
"Look at me!" she demanded.
"You took something so precious from me," she said. "You took my baby girl for no reason."
Henson told Holbert that she cannot forgive him and all she feels is hate.
"I don't understand how you could take a beautiful young girl for pretty much no reason," she said. "Would you forgive someone like that?"
"I hate you" said Kelli Bordeaux's mother. "You go to hell" pic.twitter.com/OmZQWpOBeB— Greg Barnes (@GregBarnesABC11) August 7, 2015
Bordeaux was missing for more than two years before Holbert led authorities to her remains last year. An autopsy determined she died of blunt force trauma to the head. She was 23.
Henson told Holbert that the 25 months she waited for news of her daughter were agony.
"Took you long enough to say you're sorry," she said.
Bordeaux's brother was also in the courtroom and was escorted out by deputies after repeated outbursts.
Kelli Bordeaux's brother ejected from court after outburst. pic.twitter.com/GweNs7zzaG— Greg Barnes (@GregBarnesABC11) August 7, 2015
Sheriff's detectives said Holbert was the last person to see Bordeaux alive on April 14, 2012 at the former Fayetteville night spot "Froggy Bottoms" on Ramsey Street near Interstate 295. He's a registered sex offender who was convicted as a 16-year-old of indecent liberties with a 5-year-old child.
Prosecutors say Bordeaux and Holbert were hanging out together at the bar and he agreed to give her a ride back to her apartment.
District Attorney Billy West said Holbert hit Bordeaux in the face as he was dropping her off because she confronted him about his sex offender status. The blow knocked her out.
He then took her to a makeshift camp where he was living in the woods behind Froggy Bottoms. She came too and started to yell. Holbert then beat her to death.
Bordeaux's remains were found less than a 10-minute drive away from the bar.
Read more here: Remains of Kelli Bordeaux found, Nicholas Holbert charged
Bordeaux was assigned to Fort Bragg's 601st Area Support Medical Company, 261st Multifunctional Medical Battalion, 44th Medical Brigade, as a health service specialist. Bordeaux, a native of St. Cloud, Fla., joined the military in April 2011. She arrived at the unit in November 2011.
While serving his life sentence, Holbert will receive psychiatric counseling and substance abuse treatment
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