A320 pilot reported engine vibration on takeoff resulted in return to departure airport. Post-flight inspection found engine damage due to bird ingestion.

Narrative

Immediately after TO from [RWY] XXR at ZZZ we felt and heard a vibration from our number one engine. We asked to level off to troubleshoot. All engine parameters were normal and when the power was reduced the vibration was not noticeable. While we were trying to ascertain the problem ATC informed us that several aircraft on the ground reported some sort of debris came off the back of our aircraft. We contacted Maintenance Control via Dispatch. We all agreed to return to ZZZ. Engines still indicated normal. I briefed inflight and gave them briefing information due to the uncertainty of our problem. We [requested priority handling] and complied with the overweight landing QRH. We landed normally on [RWY] XYL. Once clear of the runway we had the fire trucks visually check the aircraft and they observed nothing unusual. We then taxied back to gate XX and were towed in. After shutdown I made 2 logbook write up's. One for the initial vibration and reports of debris falling from the aircraft and the other for an overweight landing noting the touchdown weight and speed. Maintenance came to the flight deck and reported we ingested a bird in our number one engine damaging the fan blades and a portion of the rear engine casing which was the debris that was reported.Airport ops found the engine debris after a runway sweep of [RWY] XXR.