Henry, a junior who rushed for nearly 2,000 yards, is the second Alabama player to win the award.
"Since I was a kid it's been my lifelong goal and a dream of mine (to win the Heisman Trophy) and I'm just so thankful," he said.
Henry tallied 1,832 points to beat two other finalists, Stanford running back and kick returner Christian McCaffrey (1,539 points) and Clemson quarterback Deshaun Watson (1,165).
"Christian and Deshaun, keep at it. God is behind y'all," he said after accepting the trophy. "... I'm sure I'll see y'all again here next year."
Henry was overshadowed at the beginning of the season by Louisiana State's Leonard Fournette. But Heismans are often won in November. Henry excelled that month, rushing for 200 or more yards in three of four games. For the year, Henry has 1,986 yards, a total that broke Herschel Walker's Southeastern Conference record.
He thanked his teammates, especially the players who block for him.
"My offensive line, if I could have had them here I would have brought them all. They worked so hard for me," he said.
Watson has led Clemson to a 13-0 record and the College Football Playoff. The Tigers are scheduled to face the Oklahoma Sooners in the Orange Bowl on December 31. The winner will advance to the national championship game on January 11 to face either Alabama or Michigan State.
Watson, who has thrown for 3,512 yards and 30 touchdowns, hopes he emulates former Auburn quarterback Cam Newton and ex-FSU star Jameis Winston, who won both won the Heisman and the national title in the same season (12 others have done so in prior years).
McCaffrey set an NCAA Division I record for total yards in a season. The sophomore was responsible for 15 touchdowns -- eight rushing, four receiving, one kickoff return and two passing.
Henry is the first running back to win the Heisman since Alabama's Mark Ingram won in 2009.
A total of 929 votes were cast in the 2015 balloting, according to the Heisman.com website
. Most of the ballots are cast by media members (870) while 58 previous Heisman winners also vote. The public weighs in collectively as one vote.
Three points were given for a first-place vote, two points for a second-place vote and one point for a third-place ballot.