Throughout his career Hungarian cyclist Tibor Magyar represented Újpesti Dózsa, winning more than a dozen national titles on both the road and track. Magyar won his first title in 1964 when he became the Hungarian individual time trial champion. With consistent results he was eventually selected to compete in both the road race and team time trial at the 1968 Mexico City Olympics, finishing 17th in the latter with his compatriots. He continued to ride for a few more years, including competing in the road race at the 1970 UCI World Road Championships in Leicester, England.