Born in Shawnee, Oklahoma, Henry was named by Senator Barry Goldwater and Ernest "Fritz" Hollings as the national winner of the Elks Leadership Award during his high school years. Oklahoma Senators Fred R. Harris and Henry Bellmon also selected Henry as a William Randolph Hearst Foundation Scholar. He earned his Bachelor of Arts degree and Juris Doctor from the University of Oklahoma and University of Oklahoma College of Law in 1974 and 1976 respectively. While attending law school, he was elected to the Oklahoma House of Representatives, where he served until 1986. In 1986, he was elected Attorney General of Oklahoma, defeating Republican Brian C. Griffin. He was re-elected in November 1990 but resigned in June 1991 to become the dean of Oklahoma City University School of Law. Governor of OklahomaDavid Walters appointed Henry's first assistant attorney general, Susan B. Loving, to succeed him. Henry continued to serve as Dean until 1993. Henry was nominated by President Bill Clinton on February 9, 1994, to a seat on the United States Court of Appeals for the Tenth Circuit vacated by Judge William Judson Holloway, Jr.. He was confirmed by the Senate on May 6, 1994, and received commission on May 9, 1994. He served as Chief Judge from 2008 to 2010. His service terminated on June 30, 2010, due to resignation. Henry is a cousin of former Oklahoma Governor Brad Henry, and administered the oath of office at the governor's inauguration in 2003. During his service, Henry's judicial committees and activities included the United States Judicial Conference Committee on International Judicial Relations. He was named by United States Supreme Court Chief Justice William Rehnquist as Chair in 2005. In 2004, he served as part of a six-member delegation, led by Supreme Court Justice Sandra Day O'Connor, which represented the United States Judiciary at the Arab Judicial Forum. On December 10, 2009, Henry was named 17th president and CEO of Oklahoma City University, a private Methodist affiliated university with a student body of 3,700 undergraduate and graduate students. Henry became President Emeritus of Oklahoma City University in 2018, and is now in the private practice of law specializing in mediation and arbitration, conducting moot courts, and consulting on appellate advocacy. Henry is a very active civic, philanthropic, and business leader. He serves on the boards of directors for Devon Energy, Allied Arts OKC, AMAR International Charitable Foundation in the USA, Greater OKC Chamber, iCivics, Jasmine Moran Foundation Children's Museum, Oklahoma Hall of Fame, Oklahoma Medical Research Foundation, and the State Fair of Oklahoma. A life member of the National Conference of Commissioners on Uniform State Laws, Henry also has been active in the American Bar Association. His professional associations include the Council on Foreign Relations, Oklahoma Bar Association, American Law Institute, Alpha Chi National College Honor Scholarship Society and Phi Beta Kappa. He is an Independent Baptist. He was awarded an Honorary Doctor of Laws Degree from Oklahoma City University in 2000 and an Honorary Doctor of Humane Letters from the University of Tulsa in 2006. Henry has presented numerous lectures at law schools in the United States and abroad, including the 2010 Madison Lecture at New York University and the 2011 Pedrick Lecture at Arizona State University School of Law. His scholarship has been published in numerous law reviews and by the university presses of Oxford, Nebraska, and Oklahoma. He has also published widely in magazines and newspapers. He authored the "Living Our Traditions" chapter in "The Embattled Constitution," published in 2013 by New York University Press. Among his honors are Leadership Oklahoma's 2015 Lifetime Achievement Award, the Dalsimer Dean's Award by the Pepperdine School of Law, the Annual Human Rights Award by the Oklahoma Human Rights Commission, the A.C. Hamlin Award by the National Black Caucus of State Legislators, and the Humanitarian of the Year Award by the National Conference of Christians and Jews. In 2016, Kiowa Elder Bud Sahmaunt presented Henry with an honorary membership in the Kiowa Tribe of Oklahoma. He delivered the University of Oklahoma commencement address on May 12, 2017.
