A two-dimensional electron gas (2DEG) was observed in Zn polar ZnMgO/ZnO (ZnMgO on ZnO) heterostructures grown by radical source molecular beam epitaxy. Reflection high energy electron diffraction patterns taken during the growth of the ZnMgO layer remained streaky; x-ray diffraction measurements showed no evidence of phase separation for up 44 % Mg composition. These results shows that the high quality ZnMgO layers up to 44 % Mg composition were obtained without phase separation. The electron mobility of the ZnMgO/ZnO heterostructures dramatically increased with increasing Mg composition and the electron mobility (μ∼250 cm2/Vs) at RT reached a value more than twice that of an undoped ZnO layer (μ∼100 cm2/Vs) due to the 2DEG formation. The carrier concentration in turn reached values as high as ∼1×1013 cm-2 and remained nearly constant regardless of Mg composition. Strong confinement of electrons at the ZnMgO/ZnO interface was confirmed by C-V measurements with a concentration of over 4×1019 cm-3. Temperature-dependent Hall measurements of ZnMgO/ZnO heterostructures also exhibited properties associated with well defined heterostructures. The Hall mobility increased monotonically with decreasing temperature, reaching a value of 2750 cm2/Vs at 4 K. Zn polar "ZnMgO on ZnO" structures are easy to adapt to a top-gate device. These results open new possibilities for high electron mobility transistors (HEMTs) based upon ZnO based materials.