Captain reported a message ENG 1 EGT OVER LIMIT on the ECAM during approach and performed an in flight shut down of the #1 engine. The flight crew continued to landing; and after inspection taxied to the gate.

Narrative

Aircraft X. At approximately 1;900 feet AGL after the landing checklist was completed on a visual approach to Runway XXL into ZZZ; we received a message ENG 1 EGT OVER LIMIT on the ECAM. It initially went away quickly but within 5-10 seconds reappeared. The First Officer was flying with the Auto thrust and Autopilot off and thrust levers were already at idle. The ECAM directed ENG MASTER 1.....OFF. This then prompted the ENG 1 SHUTDOWN ECAM procedure. After following this procedure; we [requested priority handling] and landed on [Runway] XXL without incident. We notified ZZZ Tower that we would be stopping on the Runway. We stopped about 1;000 feet short of Taxiway 1. We called for Flight Attendants stations and after determining the engine was secured and cooling off; I called 'remain seated' 3 times over the PA. We cleared the Runway and stopped short of Taxiway 2 on 1 to wait for Crash Fire Rescue . Crash Fire Rescue approached the aircraft and we asked them to check on the number 1 engine. Crash Fire Rescue indicated that they did not see any evidence of fluid; smoke; or fire. We taxied on #2 engine and had Crash Fire Rescue follow us to Gate XX. After the parking checklist; Maintenance was called; Chief Pilot on Duty reached out to me; and a logbook entry was made.