The 17-year-old accepted responsibility, public defender Richard Simon said, and will remain in juvenile custody pending his sentencing.
The teen set papers on fire in a room at the school, and left. He is charged with arson.
Simon says the court ordered that his client undergo psychiatric and psychological testing before sentencing.
The damage estimate is now said to be about a half-million dollars, down from an earlier estimate of about $1 million.
That estimate comes from an inspection of the building that revealed significant structural damage, the district attorney's office said.
The May 24th fire was contained to the F-Pod area, school district officials said in an earlier statement, but the band storage area and classrooms on the first floor were damaged. A large part of the building was also exposed to smoke.
More than 3,000 students, along with faculty and staff, were evacuated. There were no injuries.