An elevator assembly for a harvester may include an elevator housing and an elevator extending within the elevator housing between a proximal end and a distal end. As such, the elevator may be configured to carry harvested crops between its proximal and distal ends. Furthermore, the elevator assembly may include a storage hopper extending from the elevator housing at a location adjacent to the distal end of the elevator. The storage hopper may include a conveyor extending within the storage hopper between a first end and a second end, with the conveyor configured to carry the harvested crops between its first and second ends towards a discharge opening of the storage hopper.