The information exchange among satellites is crucial for the implementation of cluster satellite cooperative missions. However, achieving fast perception, rapid networking, and high-precision time synchronization among nodes without the support of the Global Navigation Satellite System (GNSS) and other prior information remains a formidable challenge to real-time wireless networks design. Therefore, a self-organizing network methodology based on multi-agent negotiation is proposed, which autonomously determines the master node through collaborative negotiation and competitive elections. On this basis, a real-time network protocol design is carried out and a high-precision time synchronization method with motion compensation is proposed. Simulation results demonstrate that the proposed method enables rapid networking with the capability of self-discovery, self-organization, and self-healing. For a cluster of 8 satellites, the networking time and the reorganization time are less than 4 s. The time synchronization accuracy exceeds 10⁻¹⁰s with motion compensation, demonstrating excellent real-time performance and stability. The research presented in this paper provides a valuable reference for the design and application of space-based self-organizing networks for satellite cluster.