The decay $Z \rightarrow b \bar{b}$ is reconstructed in $pp$ collision data,
corresponding to 2 fb$^{-1}$ of integrated luminosity, collected by the LHCb
experiment at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The product of the
$Z$ production cross-section and the $Z \rightarrow b \bar{b}$ branching
fraction is measured for candidates in the fiducial region defined by two
particle-level $b$-quark jets with pseudorapidities in the range $2.2 < \eta <
4.2$, with transverse momenta $p_{T}>20$ GeV and dijet invariant mass in the
range $45 < m_{jj} < 165$ GeV. From a signal yield of $5462 \pm 763$ $Z
\rightarrow b \bar{b}$ events, where the uncertainty is statistical, a
production cross-section times branching fraction of $332 \pm 46 \pm 59$ pb is
obtained, where the first uncertainty is statistical and the second systematic.
The measured significance of the signal yield is 6.0 standard deviations. This
measurement represents the first observation of the $Z \rightarrow b \bar{b}$
production in the forward region of $pp$ collisions.