Jackson, who amassed 4,928 yards of total offense and 51 total touchdowns, is youngest player ever and the first player from Louisville to win the Heisman.
Wearing a school-color red coat with a black lapel, Jackson seemed a bit overwhelmed by winning.
"Oh my God," he said several times.
Among those he thanked were his teammates, saying the award was for all of them.
"I can't wait to treasure this moment with all of you," he said. "I love you guys."
Jackson told reporters he had a speech written but thanked his fellow players, coaches and mom from his heart.
"For some reason when they called my name my chest started pumping and heart started racing real hard," he said.
Jackson is the first player in major college football history with at least 3,300 passing yards and 1,500 rushing yards in a season.
He was second in the nation in points responsible per game (25.7).
"The improvement Lamar has made since coming to Louisville has been amazing," Louisville coach Bobby Petrino said. "It's all because of his dedication and hard work."
Clemson quarterback Deshaun Watson finished second in the Heisman voting, with 1,524 points. Jackson's winning total was 2,144. He received 526 of 929 first-place votes.
The other finalists were Oklahoma junior quarterback Baker Mayfield, Oklahoma senior wide receiver Dede Westbrook and Michigan junior linebacker Jabrill Peppers.