  In this paper, the $\mathcal{H}_{2}$ optimal approximation of a
$n_{y}\times{n_{u}}$ transfer function $\mathbf{G}(s)$ by a finite dimensional
system $\hat{\mathbf{H}}_{d}(s)$ including input/output delays, is addressed.
The underlying $\mathcal{H}_{2}$ optimality conditions of the approximation
problem are firstly derived and established in the case of a poles/residues
decomposition. These latter form an extension of the tangential interpolatory
conditions, presented in~\cite{gugercin2008h_2,dooren2007} for the delay-free
case, which is the main contribution of this paper. Secondly, a two stage
algorithm is proposed in order to practically obtain such an approximation.
