  We compute the two-loop corrections to the massless quark form factor
$\gamma^* \to q\bar q$ and gluon form factor $H\to gg$ to all orders in the
dimensional regularisation parameter $\epsilon=(4-d)/2$. The two-loop
contributions to the form factors are reduced to linear combinations of master
integrals, which are computed in a closed form, expressed as $\Gamma$-functions
and generalised hypergeometric functions of unit argument. Using the newly
developed HypExp-package, these can be expanded to any desired order, yielding
Laurent expansions in $\epsilon$. We provide expansions of the form factors to
order $\epsilon^2$, as required for ultraviolet renormalisation and infrared
factorisation of the three-loop form factors.
