Johnson was a 198 cm ruckman and as one of the tallest footballers to have played the game earned the nickname "Big Bob".
Johnson debuted for Melbourne at the age of 19 in 1954 and became part of the most successful era of the club's history.
After finishing with Melbourne, Johnson moved to Western Australia and joined East Fremantle where he served as captain-coach in their premiership side of 1965.
After a short stint with Subiaco, he returned to Victoria in 1970 where he joined Victorian Football Association club Oakleigh.
He became captain-coach of Oakleigh in 1971, and was the association's leading goalkicker for the home-and-away season that year[1] (he was passed by Jim 'Frosty' Miller during the finals); he then led the Devils to the premiership in 1972 at the age of 37, and subsequently to Grand Final losses in 1973 and 1974 before retiring as coach.