B737-800 Captain reported loss of oil pressure and quantity resulted in an engine shut down followed by a safe landing.

Narrative

During cruise flight at FL 380 over ZZZZ; the #2 engine Low Oil Pressure indicator illuminated; followed by secondary engine indication's indicating zero oil pressure and zero oil quantity. We also noticed an abnormal vibration with changes in engine noise. The First Officer was the pilot flying and I began the QRH procedures directing engine shutdown. I requested priority handling with ZZZZ control and requested descent to FL240. We were approximately 35-40 minutes from landing in ZZZ and the decision was made to continue to ZZZ with ATC giving us instructions to proceed direct to the airport. I briefed the crew and passengers during the decent and approaching FL180; I assumed the pilot flying duties and had the FO assume pilot monitoring duties. We were given clearance for a visual approach to RWY XX and landed without incident. Once we cleared the runway; we had ARFF (Airport Rescue and Firefighting) inspect the aircraft and they advised no visible damage or smoke. We continued with taxi to the gate and performed normal shutdown procedures without further incident.