Recollection is thought to be the hallmark of episodic memory. Here we provide evidence that the hippocampus binds together the diverse elements forming an event, allowing holistic recollection via pattern completion of all elements. Participants learn complex 'events' from multiple overlapping pairs of elements, and are tested on all pairwise associations. At encoding, element 'types' (locations, people and objects/animals) produce activation in distinct neocortical regions, while hippocampal activity predicts memory performance for all within-event pairs. When retrieving a pairwise association, neocortical activity corresponding to all event elements is reinstated, including those incidental to the task. Participant's degree of incidental reinstatement correlates with their hippocampal activity. Our results suggest that event elements, represented in distinct neocortical regions, are bound into coherent 'event engrams' in the hippocampus that enable episodic recollection--the re-experiencing or holistic retrieval of all aspects of an event--via a process of hippocampal pattern completion and neocortical reinstatement.