Solute clusters and Guinier–Preston (GP) zones play an important role in determining mechanical properties of Mg–RE (where RE represents rare earth elements) alloys. In this study, we use aberration-corrected scanning transmission electron microscopy to characterize solute clusters and GP zones in binary Mg-0.52 at.%Nd and Mg-2.32 at.%Y alloys, and rationalize the experimental observations using first-principles density functional theory computations. It is found that the solute clusters formed in the early stage of precipitation, in each of the two alloys, have a family of short-range order structures comprising [0001]α atomic columns rich in Nd or Y atoms. The separation distance of two adjacent Nd- or Y-rich columns in each structure is invariably 3.70 Å along the <>α direction. The GP zones formed in the binary Mg–Nd alloy have an irregular zig-zag mono-layer shape and a range of structures, each of which comprises solute clusters of the same or mixed types, with a unique separation distance of 6.68 Å between two adjacent clusters. GP zones also form in the binary Mg–Y alloy, but they all have a single and yet ordered structure comprising an array of regularly spaced zig-zag columns in a mono-layer rich in Y atoms, which resembles that of a single layer in the β′ phase in this alloy. The density functional theory computation results indicate that the observed arrangements of RE-rich columns within the solute clusters and GP zones are controlled by minimization of elastic strain associated with individual solute atoms.