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Abstract Gravitational waves emitted by black hole binary inspiral and mergers enable unprecedented strong-field tests of gravity, requiring accurate theoretical modeling of the expected signals in extensions of general relativity. In this paper we model the gravitational wave emission of inspiralling binaries in scalar Gauss–Bonnet gravity theories. Going beyond the weak-coupling approximation, we derive the gravitational waveform to relative first post-Newtonian order beyond the quadrupole approximation and calculate new contributions from nonlinear curvature terms. We also compute the scalar waveform to relative 0.5PN order beyond the leading −0.5PN order terms. We quantify the effect of these terms and provide ready-to-implement gravitational wave and scalar waveforms as well as the Fourier domain phase for quasi-circular binaries. We also perform a parameter space study, which indicates that the values of black hole scalar charges play a crucial role in the detectability of deviation from general relativity. We also compare the scalar waveforms to numerical relativity simulations to assess the impact of the relativistic corrections to the scalar radiation. Our results provide important foundations for future precision tests of gravity.