Gibson was born in Cameron, Texas, and received a Bachelor of Arts degree from Rice University in 1940.
He was a Sergeant in the United States Army during World War II, serving from 1942 to 1945.
In 1954, he became a judge of the Probate Court of Galveston County, Texas, and continued in that office until 1968.
Gibson was confirmed by the United States Senate on October 4, 1979, and received his commission the following day.
Gibson assumed senior status on November 1, 1989, and continued to serve in that capacity until his death on June 18, 1998, in Galveston.