Johnson was educated at Barrow Grammar School and the University of Manchester where he was awarded MScTech, Master of Arts and Doctor of Philosophy degrees supervised by H. Wright Baker.

His 1971 paper[7] with Kevin Kendall and Alan D. Roberts forms the basis of modern theories of contact mechanics.

[8] He also made significant contributions to the understanding of fluid rheology under elastohydrodynamic lubrication conditions.

[9] He received the International Award from the Society of Tribologists and Lubrication Engineers in 1983.

[12] In 1999, Johnson won the William Prager Medal awarded by the Society of Engineering Science.