Martin Johnston was born in Sydney, the son of George Johnston and Charmian Clift. With his parents, Johnston lived in England and, predominantly, Greece until 1964 when the family returned to Australia. Johnston was educated in Greek and English schools, and, after completing his high school education at North Sydney Boys' High, he entered the University of Sydney in 1966 to study Arts.

In 1968 he discontinued his studies to pursue a career in journalism. By this time his poetry was beginning to attract attention. The elegy, "Letter to Sylvia Plath", written after his mother's death in 1969 was well received, and with "The Sea-Cucumber", the elegy written after his father's death in 1970, attracted a great deal of popularity. In his review of The Sea-Cucumber (1978), Christopher Pollnitz declared the title poem one of the decade's best. Johnston's poetry did not receive universal acclaim, however, because his appreciation of several American poets, such as John Berryman, produced a style and form that saw him labelled negatively by some as a pro-American experimentalist. But his passion for ancient philosophy and formally complex writing and thinking makes such a label difficult to maintain. So, too, his legitimate status as a migrant or expatriate further complicates his poetry, making his literary position difficult to interpret.

Johnston published two collections of poetry and a collection of translated Greek folk poems in the 1970s, then spent several years in Greece, working on his poetry and the experimental novel Cicada Gambit which was eventually published in 1983. He also began work on a biography of his parents, supported by two fellowships, but did not complete the work. In the 1980s Johnston worked as a sub-editor and subtitler for SBS television, before travelling through Europe in 1988 and 1989 with his wife, Roseanne Bonney, whom he had married in 1982. His third collection of poetry, The Typewriter Considered as a Bee-Trap was published in 1983.

While in Europe, Johnson had worked productively on his poetry and a novel based on the life of the revolutionary General Makriyannis. However, Johnston died the year after he returned to Australia, leaving much work unfinished.