Gibron grew up in Indiana, where he was a standout athlete in high school. After graduating, he spent two years in the U.S. military during World War II, enrolling at Valparaiso University upon his discharge. He later transferred to Purdue University, where he played football for two years and was named an All-Big Ten Conference guard. Gibron's professional career began in 1949 with the Buffalo Bills of the AAFC. The league dissolved after that season, however, and he moved to the Browns in the NFL. While he was initially a substitute, Gibron developed into a strong lineman on Cleveland teams that won NFL championships in 1950, 1954 and 1955 behind an offensive attack that featured quarterback Otto Graham, end Dante Lavelli and tackle Lou Groza. He was named to the Pro Bowl, the NFL's all-star game, each year between 1952 and 1955.