The 28-year-old defenseman is in the final season of a three-year contract he signed with the Florida Panthers on Nov. 6, 2020, and could have become an unrestricted free agent after the season.
"It means everything," Weegar said Friday. "When I signed the deal, I just kept thinking of how long of a road it's been for me since Junior B to the [ECHL] and now to here. All my friends and family and all the support I think, it's not just me that signed the deal. It's everybody around me.
"The winning culture. … Lots of guys who have won here, and that's important. We need that down the stretch. They want to win now. I want to win now. I think everybody in this room wants to win here. The city wants to win. Passionate fanbase."
Weegar was acquired by the Flames with forward Jonathan Huberdeau in a trade that sent forward Matthew Tkachuk to the Panthers on July 22. He had 44 points (eight goals, 36 assists) in 80 regular-season games last season and one assist in 10 playoff games.
"We believe he's a top-pairing defenseman," Flames general manager Brad Treliving said of Weegar after the trade. "To me, he's just really just at the prime of his career. Is a right-shot defenseman. … We think this guy makes our team a lot better today. ... We look at him as a top-end defensemen, one of the top defensemen in the League, quite frankly."
The Flames signed Huberdeau to an eight-year, $84 million contract on Aug. 4; he could have become an unrestricted free agent after the season.
"[Huberdeau] kept giving me maybe an elbow or two in the gut saying 'When are you going to [sign]?'" Weegar said. "I kept saying the same thing to him as you guys; 'Hopefully soon.' Now maybe I can get a house next to him or something like that."
Selected in the seventh round (No. 206) of the 2013 NHL Draft, Weegar has 121 points (27 goals, 94 assists) in 306 regular-season games and five points (one goal, four assists) in 20 playoff games.
"He's a good player," Flames coach Darryl Sutter said. "He's a good player. He can play both sides. He's got a zest for the game. He's coachable. He's the right age group. He's got a lot going for him."
Calgary finished first in the Pacific Division last season before losing to the Edmonton Oilers in five games in the Western Conference Second Round. The Flames open the regular season against the Colorado Avalanche on Thursday.
"Let's go. I'm ready," Weegar said. "This is going to be fun. It's going to be a long road. It's obviously a lot of hard work and the hard work starts now. Another reason why I signed here is because I believe in this team. They want to win and we have a winning team, a winning coach, a winning culture in here. That was another important step to sign here."
NHL.com independent correspondent Aaron Vickers contributed to this report