An aggregate pier compacting system for forming a compacted aggregate pier (AP) at a target location includes a mandrel, a tamper device, and a finishing tamper device. The mandrel includes a casing for housing a drilling shaft (DS). An external vibratory hammer (EVH) repeatedly impacts a hammer element (HE) extending from the DS. The DS transfers the impact to a bore head to form a cavity at the target location. The DS is removed and the casing is filled with aggregate. The tamper device includes a compacting shaft. The EVH impacts a second HE extending from the compacting shaft and transfers the impact to a compaction head to form the compacted AP. The finishing tamper device includes a shaft. The EVH impacts a third HE extending from the shaft and transfers the impact to a finishing head compacting a top layer of the AP to form a finished AP.