Traditional high-precision satellite orbits rely on globally dense and evenly distributed ground tracking stations, while the accuracy of precise orbit determination (POD) based on a regional network cannot compare with that of a global network. Low Earth orbit (LEO) satellites can serve as space-based monitoring stations to compensate for this. In response to the current regional integrated POD that only resolves the ambiguities of ground stations, this paper proposes an ambiguity resolution (AR) strategy related to LEO satellites to enhance GPS orbit accuracy. A joint observation network is established using seven International GNSS Service (IGS) stations within China and 10 LEO satellites, including GRACE-C/D, LuTan1-A/B, SWARM-A/B/C, Sentinel-3A/B, and Sentinel-6A. Experiments are conducted and analyzed from three aspects: independent baseline selection, the common view time, and the wide-lane (WL) threshold of double-differenced ambiguity. The ambiguity fixing strategy is determined to be a combination of inter-satellite and satellite–ground baselines, a common view time of 5 min, and a WL ambiguity threshold of 0.2 cycles. Taking the final products released by the IGS as the reference, the GPS orbit accuracy in the along-track, cross-track, radial, and 1D RMS is 3.23, 2.74, 2.36, and 2.89 cm, respectively, which represents improvements of 9.3%, 12.5%, 10.9%, and 10.8% compared with the solution that only fixes the ambiguities of ground stations. This result demonstrates that, in regional integrated POD, further implementation of LEO satellite-related ambiguity fixing significantly improves GPS orbit accuracy. Given the limitation that most LEO satellites can only receive GPS satellite signals, in the future, as more LEO satellites gain access to GNSS observations, the ambiguity fixing strategy presented in this paper can provide an effective and feasible approach.