The 23-year-old Lindholm's new deal carries an annual average value of $4.85 million.
The Flames sent defenseman Dougie Hamilton, NCAA defenseman Adam Fox and left wing Micheal Ferland to the Hurricanes for center Lindholm and defenseman Hanifin, both of whom were restricted free agents.
Bill Peters was hired by the Flames as head coach after opting out of his contract with the Hurricanes after the season, so he knows Hanifin and Lindholm quite well.
Lindholm is a solid center who had 16 goals and 28 assists in 81 games last season. While he doesn't light up the scoreboard, he has been consistent -- posting between 39 and 45 points every season over the last four years.
Information from ESPN's Greg Wyshynski was used in this report.