Atomically thin two-dimensional materials have emerged as promising candidates for flexible and transparent electronic applications. Here we show non-volatile memory devices, based on field-effect transistors with large hysteresis, consisting entirely of stacked two-dimensional materials. Graphene and molybdenum disulphide were employed as both channel and charge-trapping layers, whereas hexagonal boron nitride was used as a tunnel barrier. In these ultrathin heterostructured memory devices, the atomically thin molybdenum disulphide or graphene-trapping layer stores charge tunnelled through hexagonal boron nitride, serving as a floating gate to control the charge transport in the graphene or molybdenum disulphide channel. By varying the thicknesses of two-dimensional materials and modifying the stacking order, the hysteresis and conductance polarity of the field-effect transistor can be controlled. These devices show high mobility, high on/off current ratio, large memory window and stable retention, providing a promising route towards flexible and transparent memory devices utilizing atomically thin two-dimensional materials.