Context. The Cygnus Loop (G74.0-8.5) is a very well-known nearby supernova remnant (SNR) in our Galaxy. Thanks to its large size, brightness, and angular offset from the Galactic plane, it has been studied in detail from radio to γ-ray emission. The γ-rays probe the populations of energetic particles and their acceleration mechanisms at low shock speeds.Aims. We present an analysis of the γ-ray emission detected by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope over 11 yr in the region of the Cygnus Loop.Methods. We performed detailed morphological and spectral studies of the γ-ray emission toward the remnant from 100 MeV to 100 GeV and compared it with X-ray, UV, optical, and radio images. The higher statistics with respect to the previous studies enabled us to decompose the emission from the remnant into two morphological components to model its nonthermal multiwavelength emission.Results. The extended γ-ray emission is well correlated with the thermal X-ray and UV emission of the SNR. Our morphological analysis reveals that a model considering two contributions from the X-ray and the UV emission regions is the best description of the γ-ray data. Both components show a curved spectrum, but the X-ray component is softer and more curved than the UV component, suggesting a different physical origin. The multiwavelength modeling of emission toward the SNR suggests that the nonthermal radio and γ-ray emission associated with the UV component is mostly due to the reacceleration of preexisting cosmic rays by radiative shocks in the adjacent clouds, while the nonthermal emission associated with the X-ray component arises from freshly accelerated cosmic rays.Key words: acceleration of particles / shock waves / cosmic rays / ISM: supernova remnants