Jackson represented the United States Virgin Islands at the 1979 Pan American Games, losing his first fight to Jose Baret of the Dominican Republic.
Jackson turned professional in February 1981 and had many of his early fights in Puerto Rico, where he lived for a short time, and gained a shot at WBA super welterweight champion Mike McCallum in August 1986.
After McCallum moved up to middleweight, Jackson got his second shot at the now-vacant WBA title in November 1987 against Korean Baek In-chul, winning in three rounds.
Jackson then vacated his crown, moved up to 160 lb (73 kg), and was matched against Herol 'Bomber' Graham for the vacant WBC middleweight title.
Defenses against Dennis Milton (KO 1), Ismael Negron (KO 1), and Ron Collins (TKO 5) ended quickly, but Thomas Tate would make Jackson work longer and harder in their August 1992 encounter – Julian had to go to the scorecards for the first time in a title bout in winning a 12-round unanimous decision, scoring a knockdown along the way.
The second knockdown prompted the referee to stop the fight, after Jackson made it to his feet yet remained unsteady.
Jackson had a shaky end to the first round, during which he was hurt and put under pressure until the bell by Cardamone, who wasn't considered a hard puncher.