Edwards was born in Georgetown, British Guiana (now Guyana), to a lawyer who acted as his first running coach. Following secondary school Edwards moved to the United States to pursue his running career, enrolling in New York University in 1926, and attracted attention by setting a number of intercollegiate records in middle-distance events.
While Edwards' performance at New York University clearly established him as an Olympic-calibre athlete, he was not eligible to compete for the United States even though he could compete for Canada and also did not have an Olympic team. In 1927 he was invited by Melville Marks (Bobby) Robinson, manager of the Canadian Olympic track and field team, to compete for Canada in the 1928 Summer Olympics, where Edwards won a bronze medal as part of Canada's 4 x 400m relay team.
Following Amsterdam, Edwards left New York University to attend Montreal's McGill University as a medical student, where he also competed with university's track team. Edwards also continued his association with Bobby Robinson there, competing for British Guiana in the first-ever Commonwealth Games which were created largely due to Robinson's efforts, held in Hamilton, Ontario in 1930. He would go on to compete once more for British Guiana in the 1934 British Empire Games in London.
At McGill Edwards captained the university track team from 1931 to 1936, leading the team to six consecutive championships. At the international level, Edwards went on to compete in the 1932 Summer Olympics in Los Angeles and in the infamous 1936 Summer Olympics in Berlin, where he was one of a number of black athletes, including American runner Jesse Owens, to compete before the Hitler regime. Edwards earned bronze medals in 1932 in the 800 metre, 1500 metre, and 4x400 relay event, and in 1936 in the 800 metre event. On the way back from the 1936 games, Edwards was refused lodgings in the London hotel at which the team was booked on account of his race; the full team cancelled their stay at the hotel as a result, preferring to accompany him elsewhere.
The five bronze medals gave Edwards the nickname 'Man of Bronze', and made him Canada's most prolific Olympic medal-winner; he would be joined in 2002 by speed-skater Marc Gagnon, who won five medals in three consecutive Winter Olympics, a feat also equaled by François-Louis Tremblay in the 2010 Winter Olympics. Those men were then surpassed in 2006 by speed-skater Cindy Klassen, who won six medals in two consecutive Winter Olympics, she was also joined by Clara Hughes in 2006, who won five medals over Summer and Winter Olympics between 1998–2006, and the following Olympics in Vancouver won a sixth medal. Edwards was among the first black athletes to earn an Olympic medal and, along with Hamilton runner Ray Lewis, one of only a handful of black athletes to represent Canada in the 1920s and 1930s; as a gold medal-winner for British Guiana in the 1934 British Empire Games, Edwards was also the first black man to be awarded in what are now the Commonwealth Games. Four years earlier he also participated in the 1930 British Empire Games. He finished fifth in the 880 yards event as well as in the 1 mile competition. In the 440 yards contest he was eliminated in the heats. Edwards was named the inaugural Lou Marsh Trophy winner in 1936 as Canada's top athlete.
Edwards graduated from McGill University's medical school in 1936, immediately before competing in the 1936 Olympic Games and being named Canada's top athlete. Interrupting his medical career to serve with the Canadian army, Edwards rose to the rank of captain before returning to Montreal. He earned a graduate medical diploma in 1945 and became a specialist in tropical diseases, joining the staff of Montreal's Royal Victoria Hospital and participating in a number of international medical missions. Edwards' tenure at the Royal Victoria coincided with that of infamous psychiatrist Ewen Cameron; outside his tropical medicine work, Edwards was instrumental in rescuing at least one patient whose physical illness had been misdiagnosed and mistreated by Cameron as a psychiatric matter.
Dr. Edwards was just a few days shy of his 64th birthday when he died of heart problems in 1971. He is interred in the Mount Royal Cemetery in Montreal.