Various threats posed by the progress in text-to-speech (TTS) have prompted the need to reliably trace synthesized speech. However, contemporary approaches to this task involve adding watermarks to the audio separately after generation, a process that hurts both speech quality and watermark imperceptibility. In addition, these approaches are limited in robustness and flexibility. To address these problems, we propose TraceableSpeech, a novel TTS model that directly generates watermarked speech, improving watermark imperceptibility and speech quality. Furthermore, We design the frame-wise imprinting and extraction of watermarks, achieving higher robustness against resplicing attacks and temporal flexibility in operation. Experimental results show that TraceableSpeech outperforms the strong baseline where VALL-E or HiFicodec individually uses WavMark in watermark imperceptibility, speech quality and resilience against resplicing attacks. It also can apply to speech of various durations. The code is avaliable at https://github.com/zjzser/TraceableSpeech