A300 First Officer reported a single chime and a GREEN RSVR LO LEVEL ECAM message in cruise. The flight crew continued to destination airport and made a precautionary landing. A tow team was requested to move the aircraft to the ramp.

Narrative

In cruise at FL330 450 miles from ZZZZ we got a single chime and a GREEN RSVR LO LEVEL ECAM message. We confirmed with the analog gauge on the overhead panel. Green pumps 1 and 2 off. BRK A/SKID ALTN ON. After these items were completed. We then received GREEN SYS LO PR ECAM which continuously would come on and go away. Watching the hydraulic systems page we could see the system pressurize to 2;150 PSI and deplete back to 0 as the GREEN SYS LO PR ECAM would come back up when it was at 0 PSI. We used AIRINC to talk to the Company to speak with a systems matter expert. Radio communication was unsuccessful and we continued via ACARS. Aircraft control was then transferred to the Captain. I then looked at additional information in the QRH and AOM for GREEN RSVR LO LEVEL where it confirms BRK A/SKID ALT ON and then prompts procedure increase landing distance by 1.1 and LG/GRAVITY EXTENSION. We wanted to talk to the systems matter expert to confirm this procedure needed to be performed. I then pulled up QRH for GREEN SYS LO PR in case eventually we lost green system pressure totally. Which ended up happening once the system did lose all pressure. We then performed ECAM action items and began formulating a plan together to set up for the approach and landing.We coordinated with Company for Maintenance to tug us to the ramp from either the runway or taxiway if able to exit the runway due to loss of nose wheel steering. We then coordinated with ZZZZ Center to hold at a fix about 30 miles west of the airport at 10;000 to perform the gravity extension and fully configure the airplane for landing before beginning our approach. At this time we [requested priority handling] and requested Center to coordinate with Approach and Tower for the landing and possibility of stopping on the only active runway in ZZZZ. After extensive briefing of approach; landing; alternate brake usage; possible go-around; and plan of action once stopped we requested to begin the approach. Approach and landing were uneventful. We were able to exit the runway on Taxiway XX where we were met by Airport Rescue and Firefighting (ARFF). Fire trucks began inspection of aircraft and reported smoke coming from #2 engine. We reported that we had no fire indications in the flight deck. They reported that smoke was increasing. We shut the #2 engine down at this point. At request of ARFF and ground controller we shut down engine #1 shortly thereafter. Our company mechanic then established communication with the flight deck and the tug was hooked up to the airplane. The mechanic then requested we pull the #2 engine fire handle to cut off hydraulic connection with the #2 engine. We were successfully tugged into our ramp and the flight was completed.