He also disposed of the handgun and the knife, the document said.
When Lavergne returned to Lafayette from his friend's home in New Orleans the next day, he returned to where he had left Shunick's body and buried Shunick's body in a heavily wooded area near the old cemetery.
The body was found there in August 2012 and positively identified by authorities.
"The Defendant, and his counsel, affirm and agree that this factual basis is indeed true, correct, and accurate," the end of the document reads. "The Defendant affirms and agrees that he is, in fact, guilty of the First Degree Murder of Michaela Shunick."
The document is signed by the district attorney, Lavergne and his attorneys.
The Shunick family did not respond to request for comment today, but released a statement after today's court hearing, according to The Advocate newspaper.
"My sister, Mickey Shunick, was a warrior," Shunick's sister, Charlene "Charlie" Shunick, wrote. "If it wasn't for her, our community never would have been able to bring down a dangerous man that harmed multiple people."
Shunick's mother, Nancy Anne Rowe, wrote, "She refuses to be a victim. My courageous child faced down a monster. Now I think I can face monsters too. And so can you."
In the document, Lavergne also plead guilty to killing Lisa Pate in June 1999. He met her in Lafayette, La., and "enticed and persuaded" her to go with him to a place outside of the town. They were together for several days, but when Pate said she wanted to leave, he refused to let her.
Authorities believe Lavergne killed her by putting a plastic bag over her head, the document said. Her body was found in September 1999.
Prosecutor Keith Stutes was not available for comment this afternoon but said in court today that the plea agreement required Lavergne to tell investigators where Shunick's body was and to re-enact the events surrounding the killings, according to The Advocate.