The 16-year-old, who cannot be named for legal reasons, appeared via video-link at Leeds Crown Court accused of stabbing the 61-year-old teacher to death at Corpus Christi Catholic College, in Leeds, in April.
No pleas were entered but Richard Wright QC, defending, said: "He has accepted responsibility for the unlawful killing of the deceased."
A trial on the murder charge is scheduled for November.
The teenager appeared on two video screens in the packed courtroom. He spoke twice - to confirm his name as the 10 minute long hearing began, and to acknowledge he understood what was happening, when the judge asked him at the end.
Mr Wright, Paul Greaney QC, prosecuting, and the judge, Judge Peter Collier QC, all sat in court without their normal robes.
The court heard that expert psychiatric reports would now be prepared before the trial.
Mr Wright said: "The defendant accepts that he unlawfully killed Ann Maguire.
"The issue in the case will be whether or not a partial defence is available to him."
Mr Greaney said: "It does not amount to an admission he is guilty of murder. It does amount to an admission he's guilty of manslaughter."
Both the judge and Mr Greaney asked the public to be careful about using social media to name the defendant or other details about the case ahead of the trial.
Mrs Maguire's death was the first killing of a teacher in a school since the 1996 Dunblane massacre.
The teenager was told he will appear again for a hearing on September 26. He was remanded in custody.