Top quark production in the forward region in proton-proton collisions is observed for the first time. The W+b final state with Wmunu is reconstructed using muons with a transverse momentum, p_T, larger than 25GeV in the pseudorapidity range 2.0<eta<4.5. The b jets are required to have 50<p_T<100GeV and 2.2<eta<4.2, while the transverse component of the sum of the muon and b-jet momenta must satisfy p_T>20GeV. The results are based on data corresponding to integrated luminosities of 1.0 and 2.0fb^-1 collected at center-of-mass energies of 7 and 8TeV by LHCb. The inclusive top quark production cross sections in the fiducial region are sigma(top)[7TeV]=239±53(stat)±33(syst)±24(theory)fb,sigma(top)[8TeV]=289 ±43(stat)±40(syst)±29(theory)fb.These results, along with the observed differential yields and charge asymmetries, are in agreement with next-to-leading order standard model predictions.