Born in Mount Pleasant in what was then Upper Canada, Nelles was the eldest son of William Nelles and Mary Hardy who had immigrated to Canada from New York state after the War of 1812.

He attended Victoria College in Cobourg from 1842 to 1844 and graduated from Wesleyan University in 1846, and there became a member of the Mystical Seven.

He spent a year as a principal of the Newburgh Academy in Lennox County before being ordained a minister of the Wesleyan Methodist Church in Canada in 1850.

In 1850, he was appointed professor of classics and acting principal of Victoria College.

In 1884, the school was renamed Victoria University and he would become its first chancellor and president serving until his death in 1887.