Observations of atmospheric methane (CH4) since the late 1970s and measurements of CH4 trapped in ice and snow reveal a meteoric rise in concentration during much of the twentieth century. Since 1750, levels of atmospheric CH4 have more than doubled to current globally averaged concentration near 1,800 ppb. During the late 1980s and 1990s, the CH4 growth rate slowed substantially and was near or at zero between 1999 and 2006. There is no scientific consensus on the drivers of this slowdown. Here, we report measurements of the stable isotopic composition of atmospheric CH4 (13C/12C and D/H) from a rare air archive dating from 1977 to 1998. Together with more modern records of isotopic atmospheric CH4, we performed a time-dependent retrieval of methane fluxes spanning 25 y (1984–2009) using a 3D chemical transport model. This inversion results in a 24 [18, 27] Tg y−1 CH4 increase in fugitive fossil fuel emissions since 1984 with most of this growth occurring after year 2000. This result is consistent with some bottom-up emissions inventories but not with recent estimates based on atmospheric ethane. In fact, when forced with decreasing emissions from fossil fuel sources our inversion estimates unreasonably high emissions in other sources. Further, the inversion estimates a decrease in biomass-burning emissions that could explain falling ethane abundance. A range of sensitivity tests suggests that these results are robust.