His father moved to Victoria (Australia) during the gold-digging fever, Joseph was educated at the Geelong National Grammar School.
Returning to South Australia in 1868, he was for eleven years on the staff of the South Australian Register, noted for his theatre criticisms as The Gallery Boy.
In December 1878 he purchased a half-share in the Adelaide Punch and shortly afterwards became sole proprietor.
He conducted it for several years, but the paper suffered an irreparable loss when cartoonist W.
J.
Kennedy left.
Around 1882 he became interested in gold mining and sold his interest to E.
H.
Derrington.On 8 April 1884 Johnson was elected a member to the Electoral district of Onkaparinga in the South Australian House of Assembly, and was Minister of Education and of the Northern Territory from 11 June 1887 to 27 June 1889 in the Thomas Playford II Ministry.
Johnson was the author of "Moses and Me," the record of a visit paid to the Mount Brown diggings in 1880.
Johnson held his seat of Onkaparinga until 24 April 1896.Johnson died in North Adelaide, South Australia, Australia on 18 June 1904, survived by an adopted son.