ICAO PANS-ATM (para 6.5.3.1) says that clearance for an IFR flight to execute a visual approach may be requested by a flight crew or initiated by the controller. The procedure is described for IFR flights and there is no mention of how the control service is provided.
Para 6.5.3.5 talks about separation and says 'For successive visual approaches, radar or nonradar separation shall be maintained until the pilot of a succeeding aircraft reports having the preceding aircraft in sight. The aircraft shall then be instructed to follow and maintain own separation from the preceding aircraft....
This clearly suggests to me that visual approaches were not expected to be limited to radar controlled environments when the procedure was written. The document does include a caveat that 'Controllers shall exercise caution in initiating a visual approach when there is reason to believe that the flight
crew concerned is not familiar with the aerodrome and its surrounding terrain'. This might be interpreted by some States as requiring radar monitoring of some sort to provide assurance of terrain clearance but, presumably, what the controllers' responsibilities are this would be described in national or local procedures.
For myself, I have cleared IFR aircraft for visual approaches in controlled airspace whenever the crew asked for it and the traffic situation was suitable. I don't know why but in my operational days in the State where I worked the controller was not permitted to initiate the request for a visual approach.