Hextall said Vecchione would play for the Flyers this season but is unlikely to debut against the New Jersey Devils on Saturday (7 p.m. ET; CSN-PH, MSG+, NHL.TV). Philadelphia would have four regular-season games remaining.
"I expect him to play," Hextall said. "We'll see how things go. See where we're at, and see how he practices, and see where we are health-wise, and all that stuff."
The Flyers (37-32-8) trail the Boston Bruins by six points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Vecchione, a 5-foot-10, 195-pound center, chose the Flyers over the New York Rangers and Tampa Bay Lightning, according to The Canadian Press.
He is a finalist for the Hobey Baker Award, given annually to the player voted to be the best in NCAA Division I men's ice hockey, with Northeastern forward Zach Aston-Reese (the NCAA co-scoring leader) and Denver defenseman Will Butcher.
Aston-Reese signed with the Pittsburgh Penguins on March 14. Butcher's rights are held by the Colorado Avalanche.