Gibbs was a highly recruited athlete coming out of Graham High School. He accepted a football scholarship from Texas Christian University, to become part of the school's tradition at quarterback. In college, he was a highly publicized athlete, that was usually mentioned in pre-season All-American teams, but could never reach that type of success.
In 1961, as a junior he registered 71 completions for 999 yards and 6 touchdowns. He also played a key role in beating the #1 ranked University of Texas and received the Rogers Trophy as the team MVP at the end of the season.
As a senior, he posted 89 completions for 1,013 passing yards and 9 touchdowns. He played in the East-West Shrine Game, the Hula Bowl and the Chicago College All-Star Game. As a three-year starter, he finished with 207 completions for 2,485 passing yards and 18 touchdowns.
With no first round draft choice, with their first selection in the 1962 NFL Draft, the Dallas Cowboys selected Gibbs from Texas Christian University in the second round (eighteenth overall) with a future draft pick, which allowed the team to draft him before his college eligibility was over. He was also drafted by the Denver Broncos in the second round of the 1962 AFL Draft, with a future selection.
In 1963, Gibbs entered the league as the tallest quarterback in NFL history (until 1991 when Dan McGwire broke the record). Being the third string quarterback, he wasn't activated for any game of the season. He also developed a close relationship with Don Meredith, where Gibbs tried to emulate his lifestyle. He was waived on September 3, 1964.
In 1964, he signed with the Toledo Tornadoes of the United Football League at the request of the Dallas Cowboys.
Even though he signed a three-year no-cut contract that was honored by the Dallas Cowboys, he was released before the start of the 1964 season. On October 27, 1964, because the Cowboys still held Gibbs rights, the Detroit Lions traded a fourth-round draft choice (#53-Bob Svihus) and paid over US$40,000 to be able to sign him, so he could back up Milt Plum, after Earl Morrall was lost for the year with a broken collarbone.
In 1965, he walked away from the NFL, after Gibbs was told that he was going to be traded.
In 1965, he signed with the Philadelphia Bulldogs of the Continental Football League.
In 1966, he was selected in the Continental Football League expansion draft by the Brooklyn Dodgers. He finished out his career the same year.