The strengthening mechanisms underlying the long period stacking order (LPSO) phases in Mg-Zn-Y alloys have largely remained unsolved due to unclear understanding of the local arrangements of Zn and Y atoms in the LPSO phases. The local arrangements of Zn and Y atoms in the LPSO structures are theoretically refined with first-principles method in this study. The calculations clearly demonstrate that Zn and Y atoms prefer clustering in the form of Zn6Y9 rather than arranging in random or ordered arrangements, or in the form of Zn6Y8 cluster, as proposed in previous experiments. The Zn6Y9 cluster, which leads to the formation of ABCA-type building block of the LPSO structures, can be particularly regarded as the ideal stoichiometric component of the LPSO structures. Various non-stoichiometric ZnmYn(Mg) clusters derived from the Zn6Y9 cluster can also easily exist in the LPSO structures. The non-stoichiometric ZnmYn(Mg) clusters may correspond to the arrangements of Zn and Y atoms in the LPSO phases with different Zn/Y ratios. This study indicates that the novel structures of the LPSO phases consisting of ABCA-type building blocks stem from the formation of the Zn6Y9 cluster and its derivative clusters, ZnmYn(Mg).