During the American Civil War, Goff joined the Union Army in 1861; enlisting in the 3rd West Virginia Infantry Regiment.

[2] He was also the Republican candidate for Governor of West Virginia in 1876 and 1888, but voters instead elected the Democrat.

[2] Goff was elected as a Republican from West Virginia's 1st congressional district to the United States House of Representatives of the 48th, 49th and 50th United States Congresses, serving from March 4, 1883, to March 3, 1889.

[1] He was confirmed by the United States Senate on March 17, 1892, and received his commission the same day.

[2] He was not a candidate for reelection in 1918, the first time under the Seventeenth Amendment that the seat was filled by popular vote.

[4] The World War II destroyer USS Goff was named in his honor.