White had been a restricted free agent and the new deal will keep him in Ottawa through the 2024-25 season.
"We've identified Colin as one of our core players who will help drive the team's success in both the short and long term," Senators general manager Pierre Dorion said in a team release. "Colin plays the 200-foot game that is so coveted in today's NHL. He can skate, play on both special teams, and is a character player and leader who loves hockey and this city."
The 22-year-old center had a productive 2018-19 campaign, tallying 14 goals and 41 points in 71 contests while averaging 16:12 of ice time.
Since being selected by the Senators with the 21st overall pick in the 2015 draft, the Boston College product has tallied 47 points in 97 career games.
Even with White signed, the Senators still have the fifth-lowest cap hit in the league, with $10.89 million in projected space and a nearly full roster of 22, according to CapFriendly.