Recent advancements in generative speech models based on audio-text prompts have enabled remarkable innovations like high-quality zero-shot text-to-speech. However, existing models still face limitations in handling diverse audio-text speech generation tasks involving transforming input speech and processing audio captured in adverse acoustic conditions. This paper introduces SpeechX, a versatile speech generation model capable of zero-shot TTS and various speech transformation tasks, dealing with both clean and noisy signals. SpeechX combines neural codec language modeling with multi-task learning using task-dependent prompting, enabling unified and extensible modeling and providing a consistent way for leveraging textual input in speech enhancement and transformation tasks. Experimental results show SpeechX's efficacy in various tasks, including zero-shot TTS, noise suppression, target speaker extraction, speech removal, and speech editing with or without background noise, achieving comparable or superior performance to specialized models across tasks. See https://aka.ms/speechx for demo samples.