Nelson's professional boxing debut, in 1979, did not cause much furor, except in Ghana, where he was known because of his family ties. Internationally, Nelson lacked the recognition for such an event to be given it's due importance. With the years, however, all of that changed because he garnered world wide fame as a boxer.
He beat Billy Kwame in Accra by a decision in eight to mark his professional debut. In his third fight, he fought on March 3 of 1980, he knocked out Henry Sadler in the ninth round to win Ghana's regional 126 pound title. On December 13 of that year, he knocked out Joe Skipper in round 10 to add the African continent's belt to his Ghanian regional championship.
1981 was a productive year for the young fighter. He beat Bozzou Aziza in his first fight abroad; held in Togo, and then he beat Miguel Ruiz in his first United States fight, held in California. He added the British commonwealth's Featherweight title with a five round knockout of Brian Roberts.
Despite all his early achievements and being undefeated in 13 fights, Nelson was virtually unknown outside Ghana. Because of this, he was a decisive underdog when he challenged WBC world Featherweight champion Salvador Sanchez on June 21 of 1982 at the Madison Square Garden in New York. Despite losing that fight by a knockout in round 15, Nelson's stock as a boxer rose after that fight, and he established himself as a deserving leading contender in the eyes of many fans. Sanchez sadly passed away almost two months after this fight, suffering a car accident in Mexico City. Sanchez-Nelson was Salvador Sanchez's last fight.
In his next fight, Nelson knocked out fringe contender Irving Mitchell in eight rounds.
Nelson won all four of his fights in 1983, and he began 1984 by beating Hector Cortez by decision on March 9 in Las Vegas. Then, on December 8 of that year, he became boxing royalty by knocking out Wilfredo Gomez in round 11 to win the WBC world Featherweight championship. Behind on the three judges' scorecards, Nelson rallied in that last round to become champion in Puerto Rico.
Nelson held on to that title for three years. He could not fight for 9 months after the Gomez bout, but when he returned, he retained the title in Miami with a fifth round knockout of Juvenal Ordenes in September 1985, and then in October of that year, he retained it again with a first round knockout of Pat Cowdell in Birmingham, England. The Cowdell knockout in particular became a highlight film material: Cowdell was left frozen on the canvas by Nelson's knockout punch.
In 1987, Nelson retained the title against Mauro Guitierrez, by a knockout in round six, and in a rematch with Villasana, once again, by decision. After the second fight with Villasana, Nelson abandoned the WBC's world Featherweight title.
Nelson began 1988 by fighting former Julio Cesar Chavez rival Mario Martinez for the vacant WBC's world Jr. Lightweight title. He beat Martinez by decision in 12 rounds on February 29 at Los Angeles to become world Jr. Lightweight champion, and then he defended the title with a knockout in round nine against former world champ Lupe Suarez and with a knockout in three over Sydney Del Rovere.
He proceeded in 1989 by beating Martinez in a rematch, by knockout in round 12, and then fighting Jim McDonnell, with exactly the same result. The fight with McDonnell, fought in London, was considered one of the fights of the year by many boxing magazines, and McDonnell was widely praised by critics for his stand against Nelson. McDonnell suffered four knockdowns before the fight was stopped by referee Joe Cortez.
May 19 of 1990, Nelson tried to join the exclusive group of three division world champion boxers by challenging world Lightweight champion Pernell Whitaker, but he was handled his second career loss, when Whitaker won a 12 round unanimous decision to retain the title. For his next fight, he went to Australia to meet the former world Featherweight champion, Puerto Rico's Juan Laporte. He beat Laporte by a decision in 12 to retain the world Jr. Lightweight title.
In 1991, he had only two fights. In Spain, he beat Daniel Mustapha by a knockout in round four of a non-title bout, and then, in Las Vegas, he retained the title with a controversial draw in twelve against multiple time world champion Jeff Fenech in 12 rounds. Many ringside observers and boxing writers felt Fenech had deserved to win that night, and an immediate rematch was signed and set for March 1 of 1992.
Back in Australia, Nelson defeated Fenech by a knockout in round eight of their sequel, and then he retained the title with a 12 round decision over former world champion Calvin Grove on November 7.
On February 20 of 1993, the world travelling champion defeated future world champion Gabriel Ruelas by decision in 12 in front of 120,000 fans (most of whom had come to watch Julio Cesar Chavez defend his world title against Greg Haugen in the evening's main event) in Mexico. The 120,000 fan tournout is the largest turnout ever for a boxing event. Then, on September 10, he began his four fights series with future world champion Jesse James Leija by retaining the title with a draw as part of the Chavez-Whitaker fight's undercard in San Antonio. Originally announced as a loser, Nelson found out in his dressing room that he was still world champion because the fight's announcer had accidentally mixed the scorecards and announced Leija as the winner as a result.
On May 7 of 1994, he and Leija met for the second time: That time around, the announcer was right when he announced Leija was winner and new world Jr. Lightweight champ. That was Nelson's only bout in 1994.
His first defense took place almost a year later, when he and Leija had their third bout. Nelson retained the title with a six round knockout. As had become his common practice, that was the only time Nelson fought in 1996.
In 1997, Nelson lost his title to Genaro Hernandez when beaten on points in twelve rounds. He was almost disqualified when he accidentally hit Hernandez on the back of his head after the bell to finish round seven and Hernandez lay on the floor for several minutes. However, Hernandez chose to continue, allowing Nelson to lose by the more honorable way of the judge's decision.
In 1998, he lost to Leija in their last bout, which also turned out to be his last bout. This bout was for the widely unrecognized IBA Jr. Lightweight title, but Nelson figured out his best days in boxing were over, and he retired after that. He has stayed in retirement since.
Nelson gained national hero status in Ghana. He is widely recognized by boxing fans and critics as the greatest fighter ever to come out of that coastal African nation. He was selected to the International Boxing Hall of Fame on January 8, 2004.
Nelson had a record of 39 wins, 5 losses and 2 draws, with 28 knockout wins.