The measurement of the Yarkovsky effect on near-Earth asteroids (NEAs) is common practice in orbit determination today, and the number of detections will increase with the developments of new and more accurate telescopic surveys. However, the process of finding new detections and identifying spurious ones is not yet automated, and it often relies on personal judgment. We aim to introduce a more automated procedure that can search for NEA candidates to measure the Yarkovsky effect, and that can identify spurious detections. The expected semi-major axis drift on an NEA caused by the Yarkovsky effect was computed with a Monte Carlo method on a statistical model of the physical parameters of the asteroid that relies on the most recent NEA population models and data. The expected drift was used to select candidates in which the Yarkovsky effect might be detected, according to the current knowledge of their orbit and the length of their observational arc. Then, a nongravitational acceleration along the transverse direction was estimated through orbit determination for each candidate. If the detected acceleration was statistically significant, we performed a statistical test to determine whether it was compatible with the Yarkovsky effect model. Finally, we determined the dependence on an isolated tracklet. Among the known NEAs, our procedure automatically found 348 detections of the Yarkovsky effect that were accepted. The results are overall compatible with the predicted trend with the the inverse of the diameter, and the procedure appears to be efficient in identifying and rejecting spurious detections. This algorithm is now adopted by the ESA NEO Coordination Centre to periodically update the catalogue of NEAs with a measurable Yarkovsky effect, and the results are automatically posted on the web portal.