Liam Roberts, 35, was also ordered to perform 180 hours of unpaid work and placed on the Sex Offenders Register for three years.
He had pleaded guilty previously to having 874 indecent images.
At least 18 of the pictures were Category A, the highest level.
He also admitted chatting on line with other abusers and distributing indecent pictures to others between 10 March and 27 September 2016.
Roberts, who had served in Police Scotland for eight years, resigned from the force in June this year.
At Edinburgh Sheriff Court, Roberts' solicitor, Lena Docherty, told Sheriff Kenneth McGowan the social work report described her client as at low risk of re-offending and that he had already taken steps to address his conduct.
Sheriff McGowan told Roberts: "As you will know, given your background, offending of this kind can lead to a custodial sentence, but it is quite clear from the guidance I have been given and the evidence of your undertaking rehabilitation, that the court can consider an alternative to custody."
An Edinburgh police officer caught with nearly 900 indecent images of children has been placed under supervision on a Community Payback Order for three years.