He also admitted the attempted murder of 23-year-old Raquel Jimeno and six boys and three girls aged between 12 and 16, who cannot be named due to a court order.
But he pleaded not guilty to a charge of murder, which prosecutor Christine Agnew said the Crown accepted and will deal with when the defendant returns for sentencing.
Miss Agnew said the defendant had “suffered an abnormality of the mind” at the time of the incident.
“That decision has been explained at length to the parents of Harley Watson,” she said.
Harley’s mother, who attended court with her partner, sat in the public gallery and wept as Glover gave his pleas to the charges.
Miss Agnew said the parents of the other victims and a member of staff from the school were listening to the hearing from another courtroom.
In the short hearing which lasted around 15 minutes, Miss Agnew said two psychiatrists will give evidence to the court at sentencing on January 8.
An inquest opening at Essex Coroner’s Court in Chelmsford in December last year recorded Harley’s provisional medical cause of death as a severe head injury.
The inquest heard Harley died in hospital just over an hour after he was hit by Glover’s car at around 3.20pm after school ended on the Monday afternoon.
“He was immediately conveyed to Whipps Cross Hospital where his death was confirmed at 4.43pm,” Essex coroner’s officer Lynsey Chaffe said.
Harley’s family had previously spoken of their devastation after losing their “good, kind, helpful and lovely boy”.
In a short statement released through Essex Police, Harley’s family said: “We are so devastated by what has happened.
“Harley was a good, kind, helpful and lovely boy.
“We would like to thank everyone for their kind wishes and concern.”
Reporting by PA