The 20-year-old forward, who helped the University of Denver win the NCAA championship Saturday, signed a three-year, entry-level contract Sunday and practiced for the first time Monday.
"It's been a bit of a whirlwind, it's been really busy, but it's been great," Brink said Monday. "Obviously winning the national championship was really special, and then to come here is really cool as well. It's been a really good time."
The Flyers (23-38-11), who have been eliminated from Stanley Cup Playoff contention, have 10 games remaining.
Coach Mike Yeo said he's already been impressed by Brink's package of high-end skill combined with hockey sense and competitiveness.
"The game that he brings, no question he has the ability to make plays, to create offense," Yeo said. "You draft a player like that and you know about his skill level and that's why we draft him in a high position. One of my first memories was watching him in the [2021 IIHF] World Juniors and I remember him on the penalty kill blocking shots, sort of doing whatever he could to help the team win. Obviously a character kid. Some kids, they might not get that power play opportunity that they're normally used to, but for him, he was willing to take any role and shine. So that that's a good quality to have."
Brink was selected in the second round (No. 34) of the 2019 NHL Draft. Brink led the NCAA with 43 assists and 57 points in 41 games this season as a junior, and his average of 1.39 points per game led all players. He scored 35 points (nine goals, 26 assists) during conference play, the most in the NCHC.
He was voted a finalist for the Hobey Baker Award, which went to Minnesota State goalie Dryden McKay as the top men's player in NCAA ice hockey; University of Minnesota forward Ben Meyers was the other finalist.
Yeo said he's hoping to see the same game in the NHL that made Brink successful in college.
"Don't defer," he said. "Sometimes for younger players, it can be a little bit intimidating when you're playing out there with older players and you start to ... instead of doing what is instinctual or what you should be, or more importantly taking what the other team is giving you, you start to force things and try to make plays that you think that your teammates might want you to do. So go out there and do the things that come naturally to you. And I think that if he does that he'll be fine."
Denver defeated Minnesota State 5-1 on Saturday to win the NCAA Division I men's hockey championship for the ninth time in the program's history, tying Michigan's NCAA record.
"I think it's the best way you can go out, winning with your best friends and guys you've gotten so close to for three years," Brink said. "It was awesome. It was one of the best moments of my life."
In three seasons with Denver, Brink scored 93 points (27 goals, 66 assists) in 84 games (1.10 points per game). He also scored six points (two goals, four assists) in seven game to help the United States win the 2021 WJC.
NHL.com deputy managing editor Adam Kimelman contributed to this report