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High levels of noise usually exist in today's captured images due to the relatively small sensors equipped in the smartphone cameras, where the noise brings extra challenges to lossy image compression algorithms. Without the capacity to tell the difference between image details and noise, general image compression methods allocate additional bits to explicitly store the undesired image noise during compression and restore the unpleasant noisy image during decompression. Based on the observations, we optimize the image compression algorithm to be noise-aware as joint denoising and compression to resolve the bits misallocation problem. The key is to transform the original noisy images to noise-free bits by eliminating the undesired noise during compression, where the bits are later decompressed as clean images. Specifically, we propose a novel two-branch, weight-sharing architecture with plug-in feature denoisers to allow a simple and effective realization of the goal with little computational cost. Experimental results show that our method gains a significant improvement over the existing baseline methods on both the synthetic and real-world datasets. Our source code is available at https://github.com/felixcheng97/DenoiseCompression.