Hendrickson said the deal has a max value of $57 million and contains a $16 million signing bonus.
"It means everything," Thompson told Panthers.com. "What this organization has done for me and my family, it's just tremendous. Now it's time to go to Atlanta and go get this game.
"This organization really waited to see what I could become," he added. "They understood when I was a rookie that I could come in and learn behind TD [Thomas Davis] and Luke [Kuechly] and A.J. [Klein]. That allowed me to learn the game and develop a lot more. From college to the NFL -- those first two years for me everything was happening really fast. Now the game has slowed down for me. They allowed me to learn and develop. It's a blessing."
Thompson, 25, has three sacks in 12 games this season. He is averaging more than eight tackles per game and has had double-digit tackle totals four times, including a career-high 14 in Carolina's Week 3 win at the Arizona Cardinals.
The first-round pick out of Washington has 9.5 career sacks, two fumble recoveries and an interception.
"Shaq is our type of person and our type of player," general manager Marty Hurney said in a statement announcing the extension. "He's proven that he can play linebacker at a very high level, and he's got all the traits you want. He's smart, he's physical, he can run and he's very versatile. He fits the blueprint for what we want at the position."
The move keeps Thompson from hitting the free-agent market after the season. He is now under contract through the 2023 season.
The Associated Press contributed to this report.