To improve the economy and robustness of building integrated photovoltaic (BIPV) energy system, and mitigate the negative impacts of uncertainty in photovoltaic output and electric heating and cooling loads on the economic and stable operation of BIPV energy system, this paper proposes an integrated prediction-configuration-scheduling strategy to achieve robust optimal scheduling for BIPV energy systems. Firstly, the correlation between photovoltaic output and electric heating and cooling loads is comprehensively considered by multi-task Gaussian process (MTGP), and the accurate source load prediction results and their probability information are obtained. On this basis, the MTGP-based source load uncertainty set is established. Secondly, the energy system structure is designed according to the building type and load requirements, and the economic optimal capacity allocation model is established and solved with the minimum annual investment cost and annual operational cost of the system as the objective function. Finally, the two-stage robust optimal scheduling model of BIPV energy system is established on the basis of determining the uncertainty set of source-load and equipment capacity allocation. The economic optimal scheduling scheme of the system is obtained by solving the model through column constraint generation algorithm and KKT condition. In this paper, the electric heating and cooling loads data of a teaching building in Arizona State University are used to validate the proposed optimization strategy. The simulation experimental results showed that the proposed optimization strategy can flexibly adjust the conservatism of the scheduling scheme by changing the uncertainty set confidence. Under considering the time-of-use electricity price, the energy storage devices give full play to the role of peak shaving and valley filling, which reduces the system operation cost. The proposed optimization strategy improves the economy and robustness of the scheduling scheme, compared with the traditional deterministic optimization strategy and the robust optimization strategy using box uncertainty sets.