The atmospheric nuclear testing in the 1950s and early 1960s and the burn-up of the SNAP-9A satellite led to large injections of radionuclides into the stratosphere. It is generally accepted that current levels of plutonium and caesium radionuclides in the stratosphere are negligible. Here we show that those radionuclides are present in the stratosphere at higher levels than in the troposphere. The lower content in the troposphere reveals that dry and wet deposition efficiently removes radionuclides within a period of a few weeks to months. Since the stratosphere is thermally stratified and separated from the troposphere by the tropopause, radioactive aerosols remain longer. We estimate a mean residence time for plutonium and caesium radionuclides in the stratosphere of 2.5-5 years. Our results also reveal that strong volcanic eruptions like Eyjafjallajökull in 2010 have an important role in redistributing anthropogenic radionuclides from the stratosphere to the troposphere.