Henry attended college at Washington & Jefferson, where he was an All-American tackle. In 1919, the reigning national champion Pittsburgh Panthers argued that Henry was an ineligible college player and refused to play against him. A gentleman's agreement among all college teams generally allowed players, like Henry, whose 1918 seasons were cut short by mandatory training for World War I to play. In fact, Pitt played several other teams with similarly situated players on several teams without complaint. The Panthers' stand caused an outcry among the local press and the Pitt alumni, but Henry agreed to sit out the game. In the end, Pitt won the game 7–6. In his later years, Henry was not one to keep souvenirs, but he did keep the program from that game.
Henry signed with the Canton Bulldogs on September 17, 1920. During the 1922 season while playing primarily offensive tackle with Canton, Henry, playing alongside Link Lyman and Guy Chamberlin, helped make Canton the first true powerhouse team of professional football, with a 10–0–2 record.
Despite his size and abilities at blocking, Henry was also considered one of the greatest kickers of his era. Statistics for kicks were imprecise at best during that time, however one accurate statistic was that of a 45-yard drop kickfield goal kicked by Henry on December 10, 1922. He set a professional football record with that kick that stood for twelve years. Many[who?] claimed that both Jim Thorpe and Paddy Driscoll had beaten that record, both supposedly drop-kicking field goals at 50 yards. Driscoll was alleged to have kicked two from 50 yards in one game on September 28, 1924. However, these claims could not be supported by any verifiable records. Henry was inducted into the Pro Football Hall of Fame in 1963.
In 1931, Henry was hired as the athletic director (AD) for Washington & Jefferson College, a position he held until his death in 1952. As the college and football team struggled during World War II, he served as coach in 1942 and 1945. As AD, he wanted every student to participate in some form of athletics and required every student to know how to swim. He personally raised substantial funds for the Gambolier Fund to pay for scholarships. He continued to work, even after losing a leg to diabetes.
Upon his death, Henry was eulogized in W&J's college newspaper, the Red & Black, as "capturing the very spirit of Wash Jeff and, for many people was the College."