A sheet storage apparatus and a sheet handling apparatus that allow attaching or removing of a storage bag with a simple structure and less space are provided. The sheet storage apparatus of the present disclosure includes an attachment unit including an attachment portion to which a storage bag for sheets is attached, a moving unit that moves the sheets toward an inside of the storage bag, and a first slide unit that slides at least any one of the attachment unit and the moving unit such that a relative position between the attachment unit and the moving unit is changed between a first position in which the attachment portion is covered with the moving unit and a second position in which the attachment portion is exposed to allow attaching or removing of the storage bag.