The currently observed Arctic warming will increase permafrost degradation followed by mineralization of formerly frozen organic matter to carbon dioxide (CO2) and methane (CH4). Despite increasing awareness of permafrost carbon vulnerability, the potential long‐term formation of trace gases from thawing permafrost remains unclear. The objective of the current study is to quantify the potential long‐term release of trace gases from permafrost organic matter. Therefore, Holocene and Pleistocene permafrost deposits were sampled in the Lena River Delta, Northeast Siberia. The sampled permafrost contained between 0.6% and 12.4% organic carbon. CO2 and CH4 production was measured for 1200 days in aerobic and anaerobic incubations at 4 °C. The derived fluxes were used to estimate parameters of a two pool carbon degradation model. Total CO2 production was similar in Holocene permafrost (1.3 ± 0.8 mg CO2‐C gdw−1 aerobically, 0.25 ± 0.13 mg CO2‐C gdw−1 anaerobically) as in 34 000–42 000‐year‐old Pleistocene permafrost (1.6 ± 1.2 mg CO2‐C gdw−1 aerobically, 0.26 ± 0.10 mg CO2‐C gdw−1 anaerobically). The main predictor for carbon mineralization was the content of organic matter. Anaerobic conditions strongly reduced carbon mineralization since only 25% of aerobically mineralized carbon was released as CO2 and CH4 in the absence of oxygen. CH4 production was low or absent in most of the Pleistocene permafrost and always started after a significant delay. After 1200 days on average 3.1% of initial carbon was mineralized to CO2 under aerobic conditions while without oxygen 0.55% were released as CO2 and 0.28% as CH4. The calibrated carbon degradation model predicted cumulative CO2 production over a period of 100 years accounting for 15.1% (aerobic) and 1.8% (anaerobic) of initial organic carbon, which is significantly less than recent estimates. The multiyear time series from the incubation experiments helps to more reliably constrain projections of future trace gas fluxes from thawing permafrost landscapes.