Wolfe was born in 1832 near Skibbereen, County Cork, Ireland, which at that time was part of Great Britain.

[citation needed] He entered the Church Missionary Society College, Islington, London in 1857.

[citation needed] In 1861 he was ordained a deacon at St Paul's Cathedral and in December of that year he sailed for Hong Kong from where he was assigned as a missionary minister to Fuzhou, Fujian.

[citation needed] He was ordained a priest at St John's Cathedral, Hong Kong, in 1863.

He was responsible for the building of a number of churches and schools in Fuzhou and other centres across Fukien.