The decay Z→bb¯ 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 s=8 TeV. The product of the Z production cross-section and the Z→bb¯ branching fraction is measured for candidates in the fiducial region defined by two particle-level b-quark jets with pseudorapidities in the range 2.220 GeV and dijet invariant mass in the range 45<mjj<165 GeV. From a signal yield of 5462±763 Z→bb¯ events, where the uncertainty is statistical, a production cross-section times branching fraction of 332±46±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→bb¯ production in the forward region of pp collisions.