[2][3] Born in Rustenburg District, South African Republic, Eloff was the seventh of the ten children of Sarel Johannes Eloff, commander of Rustenburg from 1864 to 1889, and his wife, Susanna Cornelia Jacobsz, and a younger brother of FC (Ryk Freek) Eloff, son-in-law of President Kruger through his marriage to Paul and Gezina Kruger's daughter Elsie.
Eloff was first educated at home by a private teacher and later visited the school of the Hermannsburg Missionary Society on the Morgenzon farm near Rustenburg.
The other members of this mission were Reverend Stephanus Jacobus du Toit (Totius's father) and General Nicolaas Smit.
Eloff remained mining commissioner until the end of December 1892 and became intimately involved with the origin and growth of Johannesburg and the early development of the Witwatersrand gold field.
[4] With the survey of Johannesburg by surveyor Jos de Villiers, the first street was named after Eloff.