Combined measurements of Higgs boson production cross sections and branching fractions are presented. The combination is based on the analyses of the Higgs boson decay modes H→γγ, ZZ∗, WW∗, ττ, bb, μμ, searches for decays into invisible final states, and on measurements of off-shell Higgs boson production. Up to 79.8 fb-1 of proton-proton collision data collected at s=13 TeV with the ATLAS detector are used. Results are presented for the gluon-gluon fusion and vector-boson fusion processes, and for associated production with vector bosons or top-quarks. The global signal strength is determined to be μ=1.11-0.08+0.09. The combined measurement yields an observed (expected) significance for the vector-boson fusion production process of 6.5σ (5.3σ). Measurements in kinematic regions defined within the simplified template cross section framework are also shown. The results are interpreted in terms of modifiers applied to the Standard Model couplings of the Higgs boson to other particles, and are used to set exclusion limits on parameters in two-Higgs-doublet models and in the simplified minimal supersymmetric Standard Model. No significant deviations from Standard Model predictions are observed.