Born in a sawmill camp known as Yellow Pine, near Many, Sabine Parish, Louisiana, Gossett moved to Texas in 1908 with his parents, who settled on a farm near Henrietta, Clay County and attended the rural schools of Clay and Garza Counties, Texas.

Gossett was elected as a Democrat to the Seventy-sixth and to the six succeeding Congresses and served from January 3, 1939, until his resignation on July 31, 1951.

According to his 1944 letterhead, he also served on the following committees as a member: Census, Territories, Insular Affairs, Revision of the Laws, and Immigration and Naturalization.

While in office, Gossett was an outspoken opponent of permitting Jewish Holocaust survivors to resettle in America, describing them as a "new Fifth Column" and the "refugee racket".

[1][2] Following his resignation from Congress, Gossett resumed the practice of law and was general attorney for the Texas Southwestern Bell Telephone Co.