His father was missionary William Patterson Alexander and mother Mary Ann McKinney.

He was named after William Radcliffe DeWitt (1792–1867) a Presbyterian pastor of his mother, who convinced her and her brother Edmund McKinney to become missionaries.

He received a BA degree from Yale in 1855 as Salutatorian, a Master of Arts in 1858,[2] and was a member of Skull and Bones.

[3] He returned to Hawaii and joined the faculty of Punahou School as a professor of Greek and history.

[5][6] In spring 1871 Alexander became Royal Surveyor-General, and Edward Payson Church replaced him as president of Punahou.

[7] Alexander with Luther Aholo represented the Kingdom of Hawaii at the International Meridian Conference, held in Washington, DC, in October 1884.

[12] Daughter Mary Charlotte Alexander (1874–1961) wrote a biography of both her grandfathers[13][14] and a history of Hawaii.