Using data from the NEMO-3 experiment, we have measured the two-neutrino double beta decay (2νββ) half-life of 82Se as T2ν1/2=[9.39±0.17( stat )±0.58( syst )]×1019 y under the single-state dominance hypothesis for this nuclear transition. The corresponding nuclear matrix element is ∣∣M2ν∣∣=0.0498±0.0016. In addition, a search for neutrinoless double beta decay (0νββ) using 0.93 kg of 82Se observed for a total of 5.25 y has been conducted and no evidence for a signal has been found. The resulting half-life limit of T0ν1/2>2.5×1023 y (90% C.L. ) for the light neutrino exchange mechanism leads to a constraint on the effective Majorana neutrino mass of ⟨mν⟩<(1.2−3.0) eV , where the range reflects 0νββ nuclear matrix element values from different calculations. Furthermore, constraints on lepton number violating parameters for other 0νββ mechanisms, such as right-handed currents, majoron emission and R-parity violating supersymmetry modes have been set.