[2][3] Through his mother, Speer was a distant relative of United States founding father Rufus King.

[4] His paternal uncle, Alexander M. Speer (1820 - 1897), was a lawyer and judge who served on the Georgia Supreme Court from 1880 until 1882.

[2][6] Eustace's father was Alexander M. Speer (1790 - 1856),[2][7] also a Methodist minister, a graduate of Emory University and one of the founders of Wesleyan College.

[6] Speer received an Artium Baccalaureus degree in classical studies in 1869 from the University of Georgia and read law.

[1] He entered the Confederate States Army in 1864 at the age of sixteen as a volunteer in the Fifth Kentucky Regiment, Lewis brigade, and remained with that command throughout the American Civil War.

[1] During his tenure, Judge Speer heard civil rights cases, and became unpopular in the white community for holding that federal law permitted protection of African Americans.

[13] In November, 1888, he wrote a letter to President-elect Benjamin Harrison and asked him for the enforcement of African-American rights during his term.

[14] During his federal judicial service, Speer also served as dean of Mercer University Law School in Macon from 1893 to 1918.