A320 Captain reported experiencing loss of G hydraulic system in cruise flight. Flight continued to destination airport and landed safely.

Narrative

During cruise flight we received above ECAM alert and corresponding low fluid indication on HYD page for G system.I confirmed FO had controls and we proceeded with Non-Normal procedures. ECAM drove us to PTU..OFF. Then GREEN ENG 1 PUMP..OFF. We finished all Non-Normals with no negative effects on flight controls while in cruise.Just Prior to this event we had an intermittent SAT phone so we contacted Dispatch who included Maintenance control. We confirmed malfunction and were directed to continue to ZZZ and they would notify ATC and CFR in advance the details of our issues.The FO and I discussed the details of our malfunction; what we could expect; as well as possibilities if our conditions deteriorated. We were still about 90 minutes our from destination. We decided to take a bathroom break and stretch while we had some time. I took the opportunity to brief the number 2 FA while I was in the galley explaining our situation. Once I returned to the cockpit I went over the details with the 1 FA. We should land normally. But in the final phase of flight is where we find out if the gravity gear drop and lock. I told her if I perceive any problems it would be close to landing and I would announce 'Cabin Crew at Stations'. I believed this occurrence would be unlikely but possible. CFR would be standing by and we would be towed to the gate.As we got into ZZZ airspace and talking with Approach; we asked for CFR to be standing by for our arrival. They were already aware of our situation and prompted us they would go ahead and handle us a priority aircraft. We informed them of our remaining fuel in lbs and souls onboard. The arrival and approach was all normal and within FAR's. We knew configuring the aircraft would take a little more time with our malfunction so I began to slow and configure the aircraft early. I was flaps 2 and roughly 180 kts when I manually gravity dropped the gear the asked for the gear handle after completion. We indicated down; 3-green and the gear page confirmed gear position. I landed smoothly without any issues. I was able to confirm immediately we had zero turn control with rudder pedals or tiller wheel. I was able to control our direction with differential braking. While using differential braking; we had plenty of runway left and I felt in good control of the aircraft and decided to slow roll to the high speed taxiway 1 - towards the end of XXR. I mentioned to the FO if I was unable to safely make the exit we would stop on the runway XXR. I was able to exit and clear the runway safely on centerline taxiway 1 and come to a complete stop. I started the APU start sequence so I could shut down both engines. I made an announcement to the passengers that we had a steering control indication on the ground and we would shut down to be towed to our gate.CFR and Maintenance approached the aircraft and made us aware we were dumping residual hydraulic fluid all over the taxiway from Engine 1. We made the decision to push the ENG 1 fire handle to close all valves to the engine. By doing this we were able to stop the flow of fluids out of engine 1. Maintenance installed gear pins on all the gears and we were towed to the gate and deplane normally.