The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double-β (0νββ) decay. We report the final results of a search for 0νββ decays with 6.914 kg of 100 Mo using the entire NEMO-3 data set with a detector live time of 4.96 yr, which corresponds to an exposure of 34.3 kg · yr. We perform a detailed study of the expected background in the 0νββ signal region and find no evidence of 0νββ decays in the data. The level of observed background in the 0νββ signal region [2.8-3.2] MeV is 0.44 AE 0.13 counts=yr=kg, and no events are observed in the interval [3.2-10] MeV. We therefore derive a lower limit on the half-life of 0νββ decays in 100 Mo of * Deceased PHYSICAL REVIEW D 92, 072011 (2015) 1550-7998=2015=92 (7)=072011 (23) 072011-1 © 2015 American Physical Society T 1=2 ð0νββÞ > 1.1 × 10 24 yr at the 90% confidence level, under the hypothesis of decay kinematics similar to that for light Majorana neutrino exchange. Depending on the model used for calculating nuclear matrix elements, the limit for the effective Majorana neutrino mass lies in the range hm ν i < 0.33-0.62 eV. We also report constraints on other lepton-number violating mechanisms for 0νββ decays.