  We derive the tensor gravitational waveform generated by a binary of
nonspinning compact objects (black holes or neutron stars) in a general class
of scalar-tensor theories of gravity. The waveform is accurate to second
post-Newtonian order beyond the leading order quadrupole approximation. We use
the direct integration of the relaxed Einstein equations formalism,
appropriately adapted to scalar-tensor theories, along with previous results
for the equations of motion in these theories. The self-gravity of the compact
objects is treated with an approach developed by Eardley. The scalar field
causes deviations from the general relativistic waveform that depend only on a
small number of parameters. Among the effects of the scalar field are new
hereditary terms which depend on the past history of the source. One of these,
a dipole-dipole coupling, produces a zero-frequency "gravitational-wave memory"
equivalent to the Christodoulou memory of general relativity. In the special
case of two black holes, the waveform reduces to the general relativistic
waveform. For a mixed (black hole-neutron star) system, the waveform is
identical to that of Einstein's theory to first post-Newtonian order, with
deviations at higher order depending only on a single parameter. The behavior
in these cases matches that found for the equations of motion.
