FUors are young stellar objects experiencing large optical outbursts due to highly enhanced accretion from the circumstellar disk onto the star. FUors are often surrounded by massive envelopes, which play a significant role in the outburst mechanism. Conversely, the subsequent eruptions might gradually clear up the obscuring envelope material and drive the protostar on its way to become a disk-only T Tauri star. Here we present an APEX $^{12}$CO and $^{13}$CO survey of eight southern and equatorial FUors. We measure the mass of the gaseous material surrounding our targets. We locate the source of the CO emission and derive physical parameters for the envelopes and outflows, where detected. Our results support the evolutionary scenario where FUors represent a transition phase from envelope-surrounded protostars to classical T Tauri stars.