We report the final results of the search for gravitationally lensed flat-spectrum radio sources found in the combination of CLASS (Cosmic Lens All-Sky Survey) and JVAS (Jodrell Bank VLA Astrometric Survey). VLA (Very Large Array) observations of 16 503 sources have been made, resulting in the largest sample of arcsec-scale lens systems available. Contained within the 16 503 sources is a complete sample of 11 685 sources which have two-point spectral indices between 1.4 and 5 GHz flatter than -0.5, and 5-GHz flux densities greater than or equal to30 mJy. A subset of 8958 sources form a well-defined statistical sample suitable for analysis of the lens statistics. We describe the systematic process by which 149 candidate lensed sources were picked from the statistical sample on the basis of possessing multiple compact components in the 0.2-arcsec resolution VLA maps. Candidates were followed up with 0.05-arcsec resolution MERLIN and 0.003-arcsec VLBA observations at 5 GHz and rejected as lens systems if they failed well-defined surface brightness and/or morphological tests. To illustrate the candidate elimination process, we show examples of sources representative of particular morphologies that have been ruled out by the follow-up observations. 194 additional candidates, not in the well-defined sample, were also followed up. Maps for all the candidates can be found on the World Wide Web at http://www.jb.man.ac.uk/research/gravlens/index.html. We summarize the properties of each of the 22 gravitational lens systems in JVAS/CLASS. 12 are double-image systems, nine are four-image systems and one is a six-image system. 13 constitute a statistically well-defined sample giving a point-source lensing rate of 1:690 +/- 190. The interpretation of the results in terms of the properties of the lensing galaxy population and cosmological parameters will be published elsewhere.