Ogbuehi attended Allen High School in Allen, Texas, where he was a two-time all-state selection for the football team. In his junior year, Ogbuehi was the best blocker for an offense that averaged 36.1 points and 225 rushing yards per game, finishing the season 15–1 with a UIL state championship. As a senior, Ogbuehi helped lead the way for an Allen offense that averaged over 466 yards per game, allowing just one sack. He was an Associated Press second-team all-state pick and unanimous first-team all-district honoree. He played in the 2010 U.S. Army All-American Bowl.
Regarded as a four-star recruit by Rivals.com, Ogbuehi was ranked as the No. 13 offensive tackle recruit in his class. He chose Texas A&M over offers from Nebraska, Kansas, Texas Tech, and Oklahoma State.
Ogbuehi was redshirted in 2010. As a freshman in 2011, he started six of 10 games at guard. As a sophomore in 2012, he started all 13 games at guard. As a junior in 2013, he was moved to the offensive tackle position.
As a senior in 2014, he received first team All-America honors from the Walter Camp Football Foundation.
As early as May 2014, Ogbuehi was projected as a high first-round selection in the 2015 NFL Draft by various mock drafts. After the NFL Combine, most analysts had projected Ogbuehi to be a first or second-round selection. Although he was invited and attended the combine, he was unable to participate in the workouts due to his ACL injury. He was ranked the seventh-best offensive tackle out of the 88 available by NFLDraftScout.com.
The Cincinnati Bengals selected Ogbuehi in the first round (21st overall) of the 2015 NFL Draft.
On June 11, 2015, the Bengals signed Ogbuehi to a four-year, $9.32 million contract with $8.72 million guaranteed and a signing bonus $5.04.
On September 1, 2015, the Bengals added Ogbuehi to the reserve/non-football injury list. They were taking extra precaution as he recovered from his ACL injury.
On December 6, 2015, Ogbuehi made his regular-season debut during the Bengals' 37–3 victory over the Cleveland Browns. He played the last five games of the season and also appeared in the Bengals' 16–18 AFC wildcard round loss to the Pittsburgh Steelers.
He started the following training camp, competing against Jake Fisher and Eric Winston for the vacant right tackle position left by Andre Smith. Ogbuehi ultimately won the job, starting the regular season as the Bengals' right tackle. He earned his first career start in the Bengals' season-opening 22–23 win over the New York Jets. Ogbuehi started the next 11 games at right tackle before being inactive for a Week 13 matchup against the Philadelphia Eagles. He made his first start at left tackle in Week 16 after struggling on the right side, moving long-time starter Andrew Whitworth to left guard for the game. He gave up two sacks that game and suffered a torn rotator cuff, ending his season.