We have recently seen tremendous progress in realistic text-to-motion generation. Yet, the existing methods often fail or produce implausible motions with unseen text inputs, which limits the applications. In this paper, we present OMG, a novel framework, which enables compelling motion generation from zero-shot open-vocabulary text prompts. Our key idea is to carefully tailor the pretrain-then-finetune paradigm into the text-to-motion generation. At the pre-training stage, our model improves the generation ability by learning the rich out-of-domain inherent motion traits. To this end, we scale up a large unconditional diffusion model up to 1B parameters, so as to utilize the massive unlabeled motion data up to over 20M motion instances. At the subsequent fine-tuning stage, we introduce motion ControlNet, which incorporates text prompts as conditioning information, through a trainable copy of the pre-trained model and the proposed novel Mixture-of-Controllers (MoC) block. MoC block adaptively recognizes various ranges of the sub-motions with a cross-attention mechanism and processes them separately with the text-token-specific experts. Such a design effectively aligns the CLIP token embeddings of text prompts to various ranges of compact and expressive motion features. Extensive experiments demonstrate that our OMG achieves significant improvements over the state-of-the-art methods on zero-shot text-to-motion generation. Project page:https://tr3e.github.io/omg-page.