The girl was reported missing on Oct. 14, after school officials contacted her parents to inform then she was not in school.
Her father told police she had been talking "to some strange male" who was not known to the girl's family or friends, the charges state.
The girl's parents posted on social media that she was missing, and police pinged her phone and determined she was traveling east.
Later on Oct. 14, the girl's mother received a Facebook post from a woman was in a relationship with Acosta-Meledez and who has two children with him.
According to the charges, the message read, "Is your daughter Haley missing. I think she is with my baby's daddy and he is bad news. He is taking her to Atlanta and Im freaking out."
West Valley City detectives eventually confirmed the girl was on a Greyhound bus to Atlanta, which was located in St. Louis, Mo.
After Acosta-Melendez's arrest, the girl told police she had been in a sexual relationship with the defendant for four months, and that she had had sexual intercourse with the defendant at least four times at his home in West Valley City, charges state.
Acosta-Melendez identified in court documents as an undocumented immigrant allegedly admitted to purchasing the bus tickets for himself and the girl by using false names.
Prosecutors said the potential sentence for transporting a minor to engage in unlawful sexual activity is 10 year to life.