Regedziński was a member of Polish team at four Chess Olympiads (1928, 1933, 1937, 1939) and at 3rd unofficial Chess Olympiad at Munich 1936. At the 2nd Chess Olympiad in The Hague 1928, he scored 10/13 (+8 –1 =4) receiving the third prize for the best individual result (no board order was known those days). In 1933, he played at third board (+2 –1 =4) at 5th Chess Olympiad in Folkestone. At the unofficial Olympiad in Munich 1936, where Polish team took the silver medal, he played at third board (+9 –2 =7). In 1937, he reached his all-time peak scoring 11/13 (+10 –1 =2) to win second prize for best result at reserve board and third best overall result at the 7th Chess Olympiad in Stockholm. In 1939, he played at fourth board, winning the individual bronze medal (+6 –3 =4) at the 8th Chess Olympiad in Buenos Aires.