Ramage, 22, just completed his senior year at the University of Wisconsin.
The Badgers captain had eight goals, 12 assists and 65 penalty minutes in 42 games.
The Flames drafted the six-foot, 195-pound defender in the fourth round of the 2010 NHL entry draft.
Ramage totalled 14 goals and 39 assists in 157 games for the Badgers.
He was captain of the U.S. junior team at the 2011 world junior hockey championship in Buffalo, N.Y., where the host country won a bronze medal.
His contract with the Flames carries a base salary of $600,000 each season. Including bonuses, it will count $900,000 annually against the salary cap.
Ramage was born in St. Louis, Mo., and is the son of Rob Ramage, a defenceman who played 15 seasons in the NHL for eight different clubs.