Using the multipolar post-Minkowskian and matching formalism we compute the gravitational
waveform of inspiralling compact binaries moving in quasi-circular orbits at the second
and a half post-Newtonian (2.5PN) approximation to general relativity. The inputs
we use include notably the mass-type quadrupole at the 2.5PN order, the mass octupole
and current quadrupole at the 2PN order, the mass \(2^5\)-pole and current \(2^4\)-pole
at 1PN. The non-linear hereditary terms come from the monopole-quadrupole multipole
interactions or tails, present at the 1.5PN, 2PN and 2.5PN orders, and the quadrupole-quadrupole
interaction arising at the 2.5PN level. In particular, the specific effect of non-linear
memory is computed using a simplified model of binary evolution in the past. The ``plus''
and ``cross'' wave polarisations at the 2.5PN order are obtained in ready-to-use form,
extending the 2PN results calculated earlier by Blanchet, Iyer, Will and Wiseman.