Intially a triple jumper and long jumper, Wells started to concentrate on the sprint events in the early 1970s. In 1978, he won two gold medals (200 m, 4 x 100 m) and a silver one (100 m) at the Commonwealth Games, and became the fastest sprinter in the UK.
Wells never used the starting blocks until a rule change forced him to do so for the 1980 Moscow Olympics. With the strong American team absent due to their boycott of the Games, Wells reached the final where he faced pre-race favourite Silvio Leonard of Cuba. In a close finish, both Wells and Leonard set a final time of 10,25, but Wells crossed the line slightly earlier to become the oldest Olympic 100 m champion at that time. The 200 m final was another close affair, but this time Wells lost to Pietro Mennea, who beat him by 0,02. With the British relay team, Wells finished 4th.
In 1982, Wells won two more Commonwealth titles in the 100 m and 200 m, but he could no longer compete with the world top. In 1984, his second Olympic appearance ended with in the 100 m semi-finals.