Atmospheric new-particle formation affects climate and is one of the least understood atmospheric aerosol processes. The complexity and variability of the atmosphere has hindered elucidation of the fundamental mechanism of new-particle formation from gaseous precursors. We show, in experiments performed with the CLOUD (Cosmics Leaving Outdoor Droplets) chamber at CERN, that sulfuric acid and oxidized organic vapors at atmospheric concentrations reproduce particle nucleation rates observed in the lower atmosphere. The experiments reveal a nucleation mechanism involving the formation of clusters containing sulfuric acid and oxidized organic molecules from the very first step. Inclusion of this mechanism in a global aerosol model yields a photochemically and biologically driven seasonal cycle of particle concentrations in the continental boundary layer, in good agreement with observations.