A search for flavour-changing neutral current decays of a top quark into an up-type quark (q = u, c) and the Standard Model Higgs boson, t → Hq, is presented. The search is based on a dataset of pp collisions at s = 13 TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider and corresponding to an integrated luminosity of 36.1 fb−1. Two complementary analyses are performed to search for top-quark pair events in which one top quark decays into Wb and the other top quark decays into Hq, and target the H→ bb¯ and H → τ+τ− decay modes, respectively. The high multiplicity of b-quark jets, or the presence of hadronically decaying τ-leptons, is exploited in the two analyses respectively. Multivariate techniques are used to separate the signal from the background, which is dominated by top-quark pair production. No significant excess of events above the background expectation is found, and 95% CL upper limits on the t → Hq branching ratios are derived. The combination of these searches with ATLAS searches in diphoton and multilepton final states yields observed (expected) 95% CL upper limits on the t → Hc and t → Hu branching ratios of 1.1 × 10−3 (8.3 × 10−4) and 1.2 × 10−3 (8.3 × 10−4), respectively. The corresponding combined observed (expected) upper limits on the |λtcH| and |λtuH| couplings are 0.064 (0.055) and 0.066 (0.055), respectively.[Figure not available: see fulltext.] © 2019, The Author(s).