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We compute the two-loop massless QCD corrections to the helicity amplitudesfor the production of two electroweak gauge bosons in the gluon fusion channel,$gg \to V_1 V_2$, keeping the virtuality of the vector bosons $V_1$ and $V_2$arbitrary and taking their decays into leptons into account. The amplitudes areexpressed in terms of master integrals, whose representation has been optimisedfor fast and reliable numerical evaluation. We provide analytical results and apublic C++ code for their numerical evaluation on HepForge athttp://vvamp.hepforge.org .

The two-loop helicity amplitudes for $gg \to V_1 V_2 \to 4~\mathrm{leptons}$