The Kilo-Degree Survey (KiDS) is an ongoing optical wide-field imaging survey with the OmegaCAM camera at the VLT Survey Telescope. It aims to image 1500 square degrees in four filters (ugri). The core science driver is mapping the large-scale matter distribution in the Universe, using weak lensing shear and photometric redshift measurements. Further science cases include galaxy evolution, Milky Way structure, detection of high-redshift clusters, and finding rare sources such as strong lenses and quasars. Here we present the third public data release (DR3) and several associated data products, adding further area, homogenized photometric calibration, photometric redshifts and weak lensing shear measurements to the first two releases. A dedicated pipeline embedded in the Astro-WISE information system is used for the production of the main release. Modifications with respect to earlier releases are described in detail. Photometric redshifts have been derived using both Bayesian template fitting, and machine-learning techniques. For the weak lensing measurements, optimized procedures based on the THELI data reduction and lensfit shear measurement packages are used. The multi-band catalogue, including homogenized photometry and photometric redshifts, covers the combined DR1, DR2 and DR3 footprint of 440 survey tiles (447deg^2^). Limiting magnitudes are typically 24.3, 25.1, 24.9, 23.8 (5 sigma in a 2 arcsec aperture) in ugri, respectively, and the typical r-band PSF size is less than 0.7 arcsec. The photometric homogenization scheme ensures accurate colors and an absolute calibration stable to ~2% for gri and ~3% in u. Separately released are a weak lensing shear catalogue and photometric redshifts based on two different machine-learning techniques.