The synthesis of complex energy systems usually involves large time series such that a direct optimization is computationally prohibitive. In this paper, we propose a decomposition method for synthesis problems using time-series aggregation. To initialize the method, the time series is aggregated to one time step. A lower bound is obtained by relaxing the energy balances and underestimating the energy demands leading to a relaxed synthesis problem, which is efficiently solvable. An upper bound is obtained by restricting the original problem with the full time series to an operation problem with a fixed structure obtained from the lower bound solution. If the bounds do not satisfy the specified optimality gap, the resolution of the time-series aggregation is iteratively increased. The decomposition method is applied to two real-world synthesis problems. The results show the fast convergence of the decomposition method outperforming commercial state-of-the-art optimization software.