The automatic generation of controllable co-speech gestures has recently gained growing attention. While existing systems typically achieve gesture control through predefined categorical labels or implicit pseudo-labels derived from motion examples, these approaches often compromise the rich details present in the original motion examples. We present MECo, a framework for motion-example-controlled co-speech gesture generation by leveraging large language models (LLMs). Our method capitalizes on LLMs' comprehension capabilities through fine-tuning to simultaneously interpret speech audio and motion examples, enabling the synthesis of gestures that preserve example-specific characteristics while maintaining speech congruence. Departing from conventional pseudo-labeling paradigms, we position motion examples as explicit query contexts within the prompt structure to guide gesture generation. Experimental results demonstrate state-of-the-art performance across three metrics: Fréchet Gesture Distance (FGD), motion diversity, and example-gesture similarity. Furthermore, our framework enables granular control of individual body parts and accommodates diverse input modalities including motion clips, static poses, human video sequences, and textual descriptions. Our code, pre-trained models, and videos are available at https://robinwitch.github.io/MECo-Page.