A321 Captain reported a hydraulic system failure and a return to their departure airport.

Narrative

On this day Aircraft X departed ZZZ early and normally. Captain as the flying pilot with FO (First Officer) assisting. It was the first flight of the day weather was VFR and good and all was normal thru the early FL20's. This was changed when the ECAM msg. HYD G RSVR LO LVL" illuminated. As per company training and procedures we initially [requested priority handling] while slowing the climb and speed. After working the immediate response items; we requested a turn back to ZZZ as the [priority] aircraft. Our Green hydraulic system Indicated empty and the gear had to be extended non normally as per the follow ups.We applied the HYD non normal to the landing app for an acceptable landing distance. A quick call was placed to the cabin to share our return plans with a planned stop on the runway for an inspection and to have the emergency equipment on standby in the event situations deteriorated. A radio call to ZZZ Operations / Maintenance which is conveniently a shared frequency to bring them up to speed on our status and return. A couple of miles from the XR LOC we deployed the gear manually so as not to be rushed. All checklists got completed and a safe landing was completed with a stop on the runway for an exterior inspection before heading to the gate. Unforeseen mechanical failure so no recommendations."