A measurement of the cross section of the associated production of a single top quark and a W boson in final states with a muon or electron and jets in proton-proton collisions at s = 13 TeV is presented. The data correspond to an integrated luminosity of 36 fb−1 collected with the CMS detector at the CERN LHC in 2016. A boosted decision tree is used to separate the tW signal from the dominant tt ¯ background, whilst the subleading W+jets and multijet backgrounds are constrained using data-based estimates. This result is the first observation of the tW process in final states containing a muon or electron and jets, with a significance exceeding 5 standard deviations. The cross section is determined to be 89 ± 4 (stat) ± 12 (syst) pb, consistent with the standard model. [Figure not available: see fulltext.]