The "remotely piloted aircraft system” (Rpas) was passed to Police Scotland by the Crown Office after being used in evidence in a criminal case.
It was no longer required and due to be destroyed.
However, the drone was of the same type as those used by Scotland’s national force so was offered to officers instead.
The move is thought to be highly unusual as money seized from criminals is channelled into supporting young people under the Scottish Government’s CashBack for Communities scheme.
The Crown Office said the police had not been offered firearms for operational use after being used as evidence in criminal cases.
Police Scotland and the Crown Office declined to provide details of the case which involved the drone.
However, there have been a series of trials involving people attempting to fly drugs and mobile phones into Scottish jails using drones.
The drone gift was revealed in a Police Scotland evaluation report on its drones to the Scottish Police Authority.
It said: “Police Scotland owns four DJI Phantom 4 systems.
“Three Phantoms were purchased initially to commence crucial flight training for officers prior to attending a national training course.
"This enabled them to gain the necessary experience and skills required to operate Rpas competently and safely.
"A fourth DJI Phantom was then given to Police Scotland from the Crown Office and Procurator Fiscal Service (COPFS).
"This machine had been seized as a production in a criminal case, was no longer required and was to be disposed of.
"On conclusion of the criminal case [it] was to be destroyed.
“However, COPFS were aware of work ongoing in Police Scotland re Rpas and offered the platform for use.”
Criminal cases involving drones have include a man being jailed for six months in January after trying to fly several mobile phones into Perth Prison by drone.
In 2018, two men received sentences of nearly three years and one year respectively for attempting to fly almost £3,000 worth of drugs into the same jail.
The previous year, a trafficker was jailed for five years after trying to smuggle heroin and mobile phones into Saughton Prison in Edinburgh.
Police Scotland said: “We're unable to provide any background on the case in question.”
The Crown Office said: “We can’t provide any details of the case that the drone came from.”
Police Scotland operates a total of seven drones, which were introduced two years ago and are based in Aberdeen, Inverness and Glasgow.
A total of 12 officers have been trained to operate the drones, which have clocked up nearly 600 hours flying time.
They were initially deployed to help search for missing people but have also been used in a wide range of cases including murder investigations, drugs operations, and after fatal industrial accidents, crashes and fires, including the Carmont train crash last August.
They have also been used to track a large gathering of drunken youths on Troon beach and monitor Greenpeace protesters occupying an oil rig in the Cromarty Firth.
However, Police Scotland has stressed they are not used for covert surveillance.