A320 Captain reported diverting after the loss of the green hydraulic system and made a precautionary landing.

Narrative

While climbing out of approximately 20;000 feet we received an ECAM G RSVR low level alert and noticed that the fluid quantity was zero. I transferred control to the First Officer and completed the ECAM actions. After referencing the QRH; there were many items now unavailable for use on landing. Among these were gravity gear extension and no nose steering upon landing. I contacted dispatch and maintenance to let them know our situation; and they advised us that ZZZ and tech ops would be ready for us upon landing. I reiterated to dispatch that we would need a tow in from the runway upon landing and was assured they would be ready. We briefly thought about diverting; but with a full load we were overweight. We elected to continue to ZZZ.We discussed at length on the flight southbound what we needed to do upon arrival. I chose not to inform inflight or the customers of the failure until closer to ZZZ. I called the #1 up to the cockpit about an hour out and explained to her we had a code yellow. I went into detail the nature of the problem and how it might affect our landing. I explained that I didn't think there would be anything abnormal on landing other than the fire trucks and being towed to the gate. Everyone was professional and did their jobs as trained. I made a PA to the customers about 40 minutes out and explained the failure in layman's terms and what they could expect on landing.Out of an abundance of caution with a hydraulic failure; I instructed the First Officer to request priority handling with ZZZ approach. After all pertinent information was exchanged we requested a 20 mile final to be sure we could get all checklist items completed before landing. On downwind we slowed and lowered the gear successfully by the gravity extension. We then configured the aircraft for landing. ATC asked if we were ready for the approach and we flew a 15 mile final to runway 10L. We reiterated to the tower that we would not be able to clear the runway upon landing. We touched down about 1500 feet down the runway and braked to a stop abeam Taxiway XX. I made a quick PA when the aircraft stopped to ask everyone to stay seated. We completed the after landing checklist; started the APU and shut down the engines. The tug then entered the runway; hooked up to us and towed us to Gate XX. The required logbook entries were made and I discussed our failure with CFR and tech ops. Tech ops said there was a major leak on top of engine number one in a hydraulic line.