Computational spectrometers utilizing disordered structures have emerged as promising solutions for meeting the imperative demand for integrated spectrometers, offering high performance and improved resilience to fabrication variations and temperature fluctuations. However, the current computational spectrometers are impractical because they rely on a brute-force random design approach for disordered structures. This leads to an uncontrollable, non-reproducible, and suboptimal spectrometer performance. In this study, we revolutionize the existing paradigm by introducing a novel inverse design approach for computational spectrometers. By harnessing the power of inverse design, which has traditionally been applied to optimize single devices with simple performance, we successfully adapted it to optimize a complex system comprising multiple correlated components with intricate spectral responses. This approach can be applied to a wide range of structures. We validated this by realizing a spectrometer utilizing a new type of disordered structure based on interferometric effects that exhibits negligible loss and high sensitivity. For a given structure, our approach yielded a remarkable 12-times improvement in the spectral resolution and a four-fold reduction in the cross-correlation between the filters. The resulting spectrometer demonstrated reliable and reproducible performance with the precise determination of structural parameters.