Mugabi was born in Kampala, Uganda, where he started to box. He won a silver medal at the 1980 Moscow Olympic games. He started as a professional on December 5, 1980, by knocking out Oemer Karadenis in round one at Kampala. Soon after that win, Mugabi moved to London, where he became acquainted with boxing promoter Mickey Duff, an expert in boxer marketing that got Mugabi various fights in England and made him a known boxer there.
Mugabi won eight fights in Europe, and then he moved to the United States, setting up residence in Florida. Over there, he became a favorite of American tv networks, beating the likes of Curtis Ramsey, Gary Guiden, former world champion Eddie Gazo, Curtis Parker, Frank The Animal Fletcher, Nino Gonzalez and Earl Hargrove. Because of his ability to fight both at Jr. Middleweight and Middleweight, fans began to talk of the possibility of him challenging either world Jr. Middleweight champion Hearns or world Middleweight champion Hagler.
By the time Mugabi was done with all those capable boxers, his knockout win streak had reached 26 in a row, without any of his professional opponents faring any better. Because of that and because of Hagler's tough battle with Hearns on April of 1985, many fans thought Mugabi had a chance to be the man to take Hagler's world Middleweight title away.
The fight finally came up on March 10 of 1986, and it was the first fight televised by Showtime. Mugabi landed his share of blows to Hagler's head, but it was Hagler who came out as the winner in the end, with a knockout in 11 rounds.
After his first loss, Mugabi went down in weight and was given an opportunity by the WBC to win their world Jr. Middleweight title, vacated by Hearns. Once again, many fans favored him, this time against Duane Thomas, on December 5 of '86. However, Mugabi suffered a broken bone below his eye as a consequence of a punch in round three, and the fight had to be stopped. Mugabi underwent through optical surgery the day after to repair his injury.
Mugabi then set off on another knockout winning streak, but, because many of his opponents after the Thomas fight were of obscure quality, he almost disappeared from the boxing map. However, in 1989, he was given another opportunity to become world champion by the WBC, and on July 8 of that year, Mugabi finally made his dream come true, knocking out Rene Jacquot in round one in Paris to become world Jr. Middleweight champion.
After two non-title wins, Mugabi put his title on the line, against Terry Norris. Mugabi became the second champion, after Al Singer, to both win and lose the world title by knockout in round one when he was defeated by Norris.
Two more wins, and Mugabi once again found himself fighting for a world title, when he faced WBO world Jr. Middleweight champion Gerald McClellan, on November 20 of 1991. Mugabi once again came out on the losing end, by a first round knockout.
Mugabi then retired for 5 years, and moved to Australia, where he still resides. In 1996, he came back and had a seven fight comeback, but, apart from beating Jamie Wallace by a decision in 12 at the Gold Coast for the Australian Middleweight title, his comeback was undistinguished. After losing to Glenn Kelly by a knockout in eight on January 16 of 1999, he finally retired for good, with a record of 42 wins, 7 losses and 1 draw, 39 wins by knockout.
His 26 fight knockout win streak stands as one of the longest knockout streaks ever in boxing.