In this work, we derive the classical effective action of bosonic string theory at order $\\\\\\\\alpha\\\\\\\'^{3}$ for the metric, Kalb-Ramond field, and dilaton by imposing a higher-derivative extension of the Buscher rules on the circular reduction of the minimal basis at this order, in the schemes where their corresponding actions at order $\\\\\\\\alpha\\\\\\\'$ are the Meissner and the Metsaev-Tseytlin schemes. We find that T-duality fixes all coupling constants in terms of the known overall factor at order $\\\\\\\\alpha\\\\\\\'$ and a single remaining parameter. This final parameter is determined by matching the single-trace term $\\\\\\\\Tr(\\\\\\\\epsilon \\\\\\\\epsilon \\\\\\\\epsilon \\\\\\\\epsilon)$ in the four-graviton S-matrix element—which lacks a massless pole—with the corresponding string theory amplitude. Our results for the Riemann quartic terms are in full agreement with those obtained from the nonlinear sigma-model approach.

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