We report the evolution of the cloud of aerosols produced in the atmosphere of Jupiter by the impact of an object in 19 July 2009 (Sánchez-Lavega et al., Astrophys. J. Lett, Vol. 715, L155. 2010). This study is based on images obtained with a battery of ground-based telescopes and the Hubble Space Telescope in the visible and in the deep near infrared absorption bands at 2.1-2.3 microns from the impact date to 31 December 2009. The impact cloud expanded zonally from 5000 km (July 19) to 225,000 km (about 180 deg in longitude by 29 October) and it was meridionally localized within a latitude band from -53.5 deg to -61.5 deg. During the first two months it showed a heterogeneous structure with embedded spots of a size of 500 - 1000 km. The cloud was mainly dispersed in longitude by the dominant zonal winds and their meridional shear and, during the initial stages, by the action of local motions perhaps originated by the thermal perturbation produced at the impact site. The tracking of individual spots within the impact cloud showed that the winds increase their eastward velocity with altitude above the tropopause by 5-10 m/s. We found evidence of discrete localized meridional motions in the equatorward direction with speeds of 1 - 2 m/s. Measurements of the cloud reflectivity evolution during the whole period showed that it followed an exponential decrease with a characteristic time of 15 days, shorter than the 45 - 200 days sedimentation time for the small aerosol particles in the stratosphere. A radiative transfer model of the cloud optical depth coupled to an advection model of the cloud dispersion by the wind shears, reproduces this behavior. Acknowledgements: ASL, RH, SPH, NBI are supported by the Spanish MICIIN AYA2009-10701 with FEDER and Grupos Gobierno Vasco IT-464-07.