The final ATLAS Run 1 measurements of Higgs boson production and couplings in the decay channel H → ZZ∗ → l+l-l'+l'-, where l, l' = e or μ, are presented. These measurements were performed using pp collision data corresponding to integrated luminosities of 4.5 and 20.3 fb-1 at center-of-mass energies of 7 and 8 TeV, respectively, recorded with the ATLAS detector at the LHC. The H → ZZ∗ → 4l signal is observed with a significance of 8.1 standard deviations, with an expectation of 6.2 standard deviations, at mH = 125.36 GeV, the combined ATLAS measurement of the Higgs boson mass from the H → γγ and H → ZZ∗ → 4l channels. The production rate relative to the Standard Model expectation, the signal strength, is measured in four different production categories in the H → ZZ∗ → 4l channel. The measured signal strength, at this mass, and with all categories combined, is 1.44+0.40-0.33. The signal strength for Higgs boson production in gluon fusion or in association with tt or bb pairs is found to be 1.7+0.5-0.4, while the signal strength for vector-boson fusion combined with WH/ZH associated production is found to be 0.3+1.6-0.9.