Cloud computing efficiency greatly depends on the efficiency of the virtual machines (VMs) placement strategy used. However, VM placement has remained one of the major challenging issues in cloud computing mainly because of the heterogeneity in both virtual and physical machines (PMs), the multidimensionality of the resources, and the increasing scale of the cloud data centers (CDCs). An inefficiency in VM placement strategy has a significant influence on the quality of service provided, the amount of energy consumed, and the running costs of the CDCs. To address these issues, in this article, we propose a greedy randomized VM placement (GRVMP) algorithm in a large-scale CDC with heterogeneous and multidimensional resources. GRVMP inspires the “power of two choices” model and places VMs on the more power-efficient PMs to jointly optimize CDC energy usage and resource utilization. The performance of GRVMP is evaluated using synthetic and real-world production scenarios (Amazon EC2) with several performance matrices. The results of the experiment confirm that GRVMP jointly optimizes power usage and the overall wastage of resource utilization. The results also show that GRVMP significantly outperforms the baseline schemes in terms of the performance metrics used.