  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.
