Dombrowski was the best ever long jumper from the former East Germany. After winning at the European cup in 1979 he won the gold medal at the 1980 Summer Olympic games in Moscow. In 1982, he was European champion. He represented the Karl-Marx-Stadt sport club. His 8.54 meter winning jump in Moscow was a low-altitude record and still stands as the German national record. At the time, it was the second best jump in history behind Bob Beamon's world record of 8.90 set in 1968.
Today he is employed as a sports teacher and works as a representative of the sports society in Schwäbisch Gmünd. On 10 April 2003, he was inducted into Germany's track and field "Hall of Fame".
During his career he was 1.87 meters tall and weighed 87 kilograms.