  We present a measurement of the $B^{0} \rightarrow D^{*-} \ell^{+}
\nu_{\ell}$ ($\ell=e,\mu$) branching ratio and of the CKM parameter $|V_{cb}|$
using signal decays accompanied by a fully reconstructed $B$ meson. The Belle
II data set of electron-positron collisions at the $\Upsilon(4S)$ resonance,
corresponding to 189.3$\,$fb$^{-1}$ of integrated luminosity, is analyzed. With
the Caprini-Lellouch-Neubert form factor parameterization, the parameters
$\eta_{\rm EW} F(1) |V_{cb}|$ and $\rho^{2}$ are extracted, where $\eta_{\rm
EW}$ is an electroweak correction, $F(1)$ is a normalization factor and
$\rho^{2}$ is a form factor shape parameter. We reconstruct 516 signal decays
and thereby obtain $\mathcal{B} (B^{0} \rightarrow D^{*-} \ell^{+} \nu_{\ell} )
= \left(5.27 \pm 0.22~\rm{\left(stat\right)} \pm
0.38~\rm{\left(syst\right)}\right) \%$, $\eta_{EW} F(1) |V_{cb}| \times 10^{3}
= 34.6 \pm 1.8~\rm{\left(stat\right)} \pm 1.7~\rm{\left(syst\right)}$, and
$\rho^{2} = 0.94 \pm 0.18~\rm{\left(stat\right)} \pm
0.11~\rm{\left(syst\right)}$.
