  Gravitational waves emitted by black hole binary inspiral and mergers enable
unprecedented strong-field tests of gravity, requiring accurate theoretical
modelling of the expected signals in extensions of General Relativity. In this
paper we model the gravitational wave emission of inspiraling binaries in
scalar Gauss-Bonnet gravity theories. Going beyond the weak-coupling
approximation, we derive the gravitational waveform to first post-Newtonian
order beyond the quadrupole approximation and calculate new contributions from
nonlinear curvature 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.
