Zn-Mg alloys are considered to have potential application in bone implants, since both metals are biocompatible and have biodegradable characteristics. Adding Mg to Zn can boost mechanical and corrosion resistances. However, the literature is very limited on quantifying the interrelation of solidification parameters, microstructural features and mechanical/corrosion properties of Zn-Mg alloys. The present study examines the interrelations of alloy Mg content, macrosegregation effects, morphology and scale of the matrix and eutectic phases, nature of intermetallics and tensile and corrosion properties of near-eutectic Zn-Mg alloys. The alloys samples are obtained by unsteady-state directional solidification resulting in a wide range of solidification thermal parameters and microstructures. We examine microstructural features of both dendritic and complex regular eutectic phases. It is shown that the eutectic exhibits a bimodal pattern with neighboring areas of coarse and fine lamellae. Experimental growth laws relating the primary, secondary and eutectic spacings to the solidification cooling rate and growth rate are proposed. Hall-Perch type equations are derived expressing tensile strength and elongation to dendritic and eutectic spacings. Electrochemical parameters determined by polarization curves during corrosion tests and SEM analyses of corroded areas have shown that the alloy having an essentially eutectic microstructure is associated with better corrosion resistance.