Light Transport
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 66; Flight Crew Total 35447; Flight Crew Type 2600
Situational Awareness
Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Aircraft Equipment Problem Dissipated; Flight Crew Overcame Equipment Problem; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors
While descending being radar vectored and level 14;000 feet; ATC asked if we had EKO in sight. We responded affirmative.  Then we both heard 'cleared for the visual approach EKO.  We were in VISUAL conditions had the terrain and the airport in sight; started a descent then received a warning from ATC that they were getting a low altitude alert.  We advised that we were in visual conditions and had the terrain in sight and continued our visual approach.
Light Transport aircraft Captain reported ATC issued a low altitude warning during visual approach to EKO airport. Captain replied that airport and terrain in sight. Flight executed an uneventful landing.