JPEG reversible data hiding (RDH) refers to covert communication technology to accurately extract secret data while also perfectly recovering the original JPEG image. With the development of cloud services, a large number of private JPEG images can be efficiently managed in cloud platforms by embedding user ID or authentication labels. Nevertheless, data embedding operations may inadvertently disrupt the encoding sequence of the original JPEG image, resulting in severe distortion of the host image when it is re-compressed to JPEG format. To address this problem, this paper proposes a new JPEG RDH scheme based on block sorting optimization and dynamic iterative histogram modification. We firstly design a block ordering optimization strategy by combining the number of zero coefficients and the quantization table values of non-zero coefficients in a DCT block. Subsequently, a dynamic iterative histogram modification scheme is proposed by considering the local features and embedding capability of histograms generated from different texture images. According to the given payloads, we introduce different parameters to control the iterations of two-dimensional histogram and then adaptively generate the optimal histogram modification mapping, which can realize low JPEG file size increments by guaranteeing most of the AC coefficients unchanged as much as possible. Numerous experiments have shown that our scheme can achieve an effective balance among embedding capacity, visual quality, file size increment, computational complexity, and outperforms the state-of-the-arts in terms of the above metrics.