Anthony Fuggle was a classics master at Colet Court, Barnes, south-west London.
He admitted six counts of possessing indecent images of children, and seven of making indecent images of children on or before 10 September 2013.
He was found to be in possession of more than 1,000 still and moving images of children.
The 58-year-old was a teacher at the school, which is a junior division of St Paul's Preparatory School.
Alumni include Chancellor George Osborne.
Investigations also revealed he had downloaded almost 2,000 images of youngsters, some of whom were as young as 12, and which included topless boys in shorts, boys on a beach, and some who were naked.
Four counts of making indecent images of the most severe level, Category A, were left to lie on file after he pleaded not guilty to them.
Fuggle appeared at Kingston Crown Court and the case was adjourned until 5 June for sentencing.
Jane Humphryes QC said he had been seeking help and was attending weekly therapy sessions.
Fuggle was released on bail on the conditions that he does not go to Colet Court school, or be in the company of anyone under the age of 16 unless supervised.
The former teacher from Sutton in Surrey is understood to have resigned from his post at the school after he was arrested in September 2013.
He was the first person to be charged under the Metropolitan Police's Operation Winthorpe.
The investigation was set up to investigate allegations of historical sexual abuse and misconduct at St Paul's and Colet Court.
A former teacher at an elite boys' school has pleaded guilty to possessing and making thousands of indecent images of children.