"This case has haunted us since February. This arrest is a huge relief for us, this very brave girl, her parents, the school and the neighborhood," Pedersen said. "We're very happy about this this is a big win."
Johnson, whose prior criminal history included burglary, theft and fraud offenses but not sexual crimes, was to be booked into Utah County Jail on suspicion of first-degree felony counts of child rape, aggravated sexual abuse of a child and child kidnapping.
If convicted, those offenses each a carry maximum prison term of up to life behind bars.
The girl was walking to classes on Feb. 5 and was just 20 yards from the school doors when the suspect approached her, telling her she could not use that entrance. Claiming he would show her the right entrance, he allegedly then led her away and forced her behind the trash bin and raped her.
The assailant then fled the scene, and the girl ran to school and told a teacher what had happened. The teacher then called 911.
Orem officers recovered footprints from the snow, and the DNA evidence was collected from the girl.
On Wednesday, the state crime laboratory notified Orem detectives that it had recovered DNA that matched that of Johnson already on record with the FBI's Combined DNA Index System (CODIS).
Pedersen said that during questioning, Johnson did not admit to the crimes, but the apparently evolving alibis he gave detectives failed to hold up to scrutiny.
A search warrant was obtained and investigators allegedly found clothing similar to that described by the girl, as well as shoes police say matched the prints found earlier.