We present the closed analytic expression of the form factors of the
two-loop QED vertex amplitude for on-shell electrons of finite mass $m$
and arbitrary momentum transfer $S=-Q^2$. The calculation is carried out
within the continuous $D$-dimensional regularization scheme, with a single
continuous parameter $D$, the dimension of the space-time, which
regularizes at the same time UltraViolet (UV) and InfraRed (IR)
divergences. The results are expressed in terms of 1-dimensional harmonic
polylogarithms of maximum weight 4.
