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Understanding, predicting, and ultimately controlling exciton band structure and exciton dynamics are central to diverse chemical and materials problems. Here, we have developed a first-principles method to determine exciton dispersion and exciton–phonon interaction in semiconducting and insulating solids based on time-dependent density functional theory. The first-principles method is formulated in planewave bases and pseudopotentials and can be used to compute exciton band structures, exciton charge density, ionic forces, the non-adiabatic coupling matrix between excitonic states, and the exciton–phonon coupling matrix. Based on the spinor formulation, the method enables self-consistent noncollinear calculations to capture spin-orbital coupling. Hybrid exchange-correlation functionals are incorporated to deal with long-range electron–hole interactions in solids. A sub-Hilbert space approximation is introduced to reduce the computational cost without loss of accuracy. For validations, we have applied the method to compute the exciton band structure and exciton–phonon coupling strength in transition metal dichalcogenide monolayers; both agree very well with the previous GW-Bethe–Salpeter equation and experimental results. This development paves the way for accurate determinations of exciton dynamics in a wide range of solid-state materials.