In this work, we report on the observation of resistive switching in the nanocrystalline Tellurium oxide (TeOx) in ITO/TeOx/Ag device configuration. The TeOx films grown in an O2/Ar environment have dominant β-TeO2 along with other polymorphs and amorphous TeO2. From the resistive switching characteristics, it is suggestive that the β-TeO2 phase promotes the conductive filament formation across the highly insulating amorphous matrix. The memory device demonstrates bipolar resistive switching with excellent endurance, retention and on-off ratio. The device also features formation-free switching with low set and reset voltage (0.6 V and -0.8 V respectively) and displays multilevel switching upon varying compliance current. I-V characterization clarifies the conduction path is indeed filamentary type. The result highlights that TeOx can be a prominent resistive switching material for memory and brain-inspired computing devices.