Both meteorology and optical conditions are crucial for selecting the best site to host extremely large telescopes such as the Thirty Meter Telescope (TMT) and the European project (E-ELT). For the E-ELT, a year-long meteorological campaign was performed at our two reference sites, the Observatorio del Roque de los Muchachos (ORM) and Cerro Ventarrones (very close to the VLT site at Paranal), and at other sites also considered as alternatives to the reference sites: Aklim, Macón, and Izaña (Observatorio del Teide; OT). In this article, we present a statistical analysis of the ground meteorological properties recorded at these sites, making use of automatic weather stations (AWSs) equipped with standard meteorological sensors providing the air temperature, relative humidity, barometric pressure, wind speed, and wind direction, using standard procedures across all sites. Meteorology offers but one discriminant in the complicated question of where to site such a major facility as the E-ELT (other factors being seeing, local geology, the economics of the logistics, etc.), both for determining the feasibility of telescope and instrumentation design and construction and for determining the useful observing time. However, the final decision of where to locate a major telescope depends in part on all these—and other—considerations and not on any one criterion alone. In summary, for 90% of the nighttime, the wind speed is lower than 18 m s-1, the telescope operational limit at all the sites except Macón. For this reason, Macón was discarded in the final site selection as, for 25% of the time, the wind speed is greater than 17 m s-1. The smallest nighttime temperature gradient is at ORM, whereas the lowest mean relative humidity value is reached at the Ventarrones site. Izaña was discarded in the site selection study from the very beginning due to lack of funding to install further site-testing equipement (e.g., Multi-Aperture Scintillation Sensor-Differential Image Motion Monitor (MASS-DIMM)). We investigate the statistical distributions of annual and monthly meteorological conditions for day and night separately. This is the third paper in a series discussing the E-ELT FP6 site characterization project.