Air carrier flight crew reported hydraulic system failure during departure climb. Flight crew diverted and returned to departure airport and landed uneventfully.

Narrative

FO (First Officer) Takeoff from runway XXR at ZZZ was normal. After rotation; the pilot flying (FO) called for landing gear up. The landing gear was raised immediately; and within 2-3 seconds; the tower called to inform us that we were trailing a significant amount of smoke from what appeared to be one of the engines (We later learned that it was actually hydraulic fluid from the right landing gear well when a line separated; and it completely depleted the green hydraulic system in a short amount of time). At that same time there was a noticeable load rumbling. We were approaching 3000 feet and the CA (Captain) asked Tower to level off. Almost immediately; we begin getting ECAMS. The first one was HYD green reservoir low level. Then almost immediately L/G doors not closed with associated warnings and other associated warnings about gear; spoilers; airspeeds; etc. After reviewing the QRC and determining that this condition was not an immediate action or ECAM exception. the CA assigned the me to continue flying duties and I directed ECAM actions. I informed the Tower that we would need to return immediately and the CA set up the MCDU (Multipurpose Control Display Unit) for an immediate return with ZZZ as the new destination; I configured the box for an approach to runway XXR at ZZZ. Tower switched us over to departure for coordination. The CA [requested priority handling] with Departure and requested equipment meet us upon landing. Departure allowed us to fly a long downwind with speed at our discretion while we analyzed and addressed our situation and took appropriate actions.The CA commenced the ECAM instructions and turned off the green hydraulic pump then the PTU (Power Transfer Unit); and other actions per the ECAM. We received vectors back to runway XXR. We had a jump-seater who was a new hire Pilot who had just finished OE (Operating Experience) and had considerable Airbus experience. He assisted us by performing a landing assessment and raising our attention to details on the ECAM; He was actually very helpful. We all remained calm and completed configuring and discussed the systems we had lost including spoilers 1 and 5; reverse on number one engine; normal brakes ( no Anti-skid); auto braking; and components on the green hydraulic system. We reviewed all the systems Lost and the status pages; then commenced with descent checklist; and before Landing Checklist configuring with full flaps. FO flew a normal approach and reported the controls felt a bit mushy". Weather was not a factor with light winds. The FO landed in the normal landing zone initiated reverse with the one engine reverser; and immediately began breaking. We cleared the runway at taxi way 1 and were met by the emergency responders. Parking brake was set and after the APU was started; we shut engines down and asked for the fire chief to visually evaluate our condition. He reported hydraulic fluid was leaking and puddling below the aircraft but mostly out of the right landing gear. There was no smoke or indication of imminent fire so we allowed the fire department to more thoroughly assess and decided to get towed back into the gate. We were approximately 3000 pounds over max landing weight (Maintenance control was notified and a report submitted for overweight landing) and we did a quick review of the overweight Landing QRH to include go around considerations. Once maintenance arrived at the airplane with a tug we retrieved the landing gear locking devices and nose gear pin; and dropped them out of the flight deck window; avoiding contact with the aircraft. They secured all the landing gear and commence to tow us back to gate. We took a different plane to ZZZ1 without incident.Catastrophic failure of the hydraulic line/joint.A catastrophic hydraulic line/joint failure that the crew had no way to know it was going to occur."