Weber will be sentenced on May 28. He is facing five years to life in prison on each count.
On Tuesday, Weber hung his head during much of the short proceeding, and when 4th District Court Judge Lynn Davis asked Weber for his plea on each count, the word "guilty" was nearly an inaudible whisper.
Assistant Utah Attorney General Paul Amann said Tuesday outside of court that Weber's plea deal was a good thing because the victim wanted to remain anonymous, and did not want to testify in court.
Though the case may be close to resolution, Weber's legal issues are likely far from over, as Amann said other alleged victims have come forward with similar allegations.
Amann would not detail how many alleged victims have spoken with his office, but said crimes may have taken place in several counties in Utah. No other sexual abuse cases had been filed against Weber as of Tuesday.
Court papers say authorities launched their investigation last fall after a 48-year-old man contacted police to report that he had been sexually abused by Weber between 1975 and 1977. The man, who is not identified in court papers, was then 11 years old and was a student in Weber's class, court papers said.
In a probable cause statement also filed with the court, FBI investigator Jeffrey Ross said Weber acknowledged in an interview that he had sexually assaulted several male students over the past 35 years, including the most recent alleged victim, court papers said.