It is a popular practice that adopting forecast information to improve the efficiency of hybrid power systems, however, resulting in error accumulation along the predictors, forecast models, and operation models. To cope with this issue, complementary operating rules integrated with teleconnection factors were developed for hydro-photovoltaic (PV) hybrid power plants. First, individual and common teleconnection factors, which dominate variations of streamflow and PV output, were identified using Pearson correlation coefficients. Then, three types of operating rules using stochastic optimization integrated with teleconnection factors were proposed. Specifically, teleconnection factors are adopted as state variables in stochastic dynamic programming (SDP), independent variables in implicit stochastic optimization based on linear fitting (LF-ISO) and classification bases in implicit stochastic optimization based on K-Nearest Neighbor (KNN–ISO). China's Longyangxia hydro-PV hybrid power plant was chosen as case study. Results show that (1) Teleconnection factors including Asia Polar Vortex Intensity Index and North Atlantic Oscillation dominate streamflow and PV output; (2) The proposed operating rules realize direct relationship mapping from teleconnection factors to operation decisions, and increase total power generation by 0.070–0.369 billion kWh when compared with same type rules using forecast scenarios; (3) SDP is preferred for Longyangxia hydro-PV hybrid power plant regardless of forecast categories.