William Johnson had the bad luck of swimming on two winning relay teams without receiving an actual gold medal. Unlike in modern Games, in 1968 no gold medals were awarded to swimmers who only competed in the heats. Johnson competed in the lead-off legs of both the 4 x 100 m and 4 x 200 m freestyle relays, that were both won by the US team. Johnson swam for La Habra High School, graduating in 1964, and then attended the University of Southern California, swimming for them through 1969. At the 1967 NCAAs he third in the 200 free, fourth in the 100 fly, and sixth in the 200 IM, making All-American in all three events. In 1968, he placed fifth in the 200 yard freestyle at the NCAAs and was third in the 200 free at the AAU Championship.