Wheeler was born in Warwick, New York, the son of a Methodist minister who moved frequently.
At the age of 19 William found work as an apprentice printer and reporter for the Ohio Statesman under Samuel Medary.
He also studied law in his spare time, and in 1848 he was admitted to practice in front of the bar.
Wheeler was appointed as United States Marshal of Montana Territory on May 15, 1869, succeeding Neil Howie.
Wheeler was a founding officer of the Montana Historical Society, and served as the organization's librarian from 1884 until his death in 1894.