DeBrincat has one season remaining on a three-year, $19.2 million contract (average annual value $6.4 million) he signed Oct. 3, 2019 before he can become a restricted free agent.
Dorion said the Senators will begin their attempts to sign DeBrincat to a contract extension once they're eligible to do so on July 13.
"We can control him for two years," Dorion said. "Obviously, we would like to extend him at some point in time, but you've got to make sure the fit is all right. He was pretty excited. He talked to both myself and (Senators coach) D.J. (Smith) earlier and he was really excited. He knows we've got a good young group of players. He's played five years in the League and I think right now there was a bit of shock for him, but once July 13 passes we can start talking with his representative and we'll do that."
DeBrincat said he hadn't thought about a new contract yet.
"I think we'll see what happens," he said. "I don't really have an answer for you right now. It's been a whirlwind couple of days. I'll start to think about that a little bit later."
DeBrincat, who played in the NHL All Star Game this season, was a second-round pick (No. 39) in the 2016 NHL Draft. He has 307 points (160 goals, 147 assists) in 368 regular-season games and six points (two goals, four assists) in nine Stanley Cup Playoff games all with Chicago.
"He's an electric player that is really, really competitive," Senators coach D.J. Smith said. "He scores, that's for sure, but he tracks, he works. He's a player that is going to fit in really well with our young group and it's an exciting time for them all to be together.
"Just naturally your first thought is you'd like to see him play with Timmy [Stutzle] a little bit for the amount of speed he has and the way Timmy carries the puck through the middle of the ice. As the year goes we know things change but my first thought is he'd be a real nice fit with Tim."
The Blackhawks selected defenseman Kevin Korchinski at No. 7. They later traded for the No. 13 pick, sending center Kirby Dach to the Montreal Canadiens. Chicago used that pick to select center Frank Nazar.
"We thank Alex for his tireless dedication to the Blackhawks organization over the last five seasons and wish him the best in Ottawa," Blackhawks GM Kyle Davidson said. "It was an incredibly difficult decision to trade a player of Alex's caliber. We feel as if this move sets the Blackhawks up for future success by giving us additional flexibility and future talent. Securing this early of a first-round pick for tonight and an additional second-round selection tomorrow allows us to fortify our prospect base with high-end players who we expect to be difference makers in the coming years."
Dorion said acquiring DeBrincat is a significant step in the Senators moving out of a rebuild and into a new phase of attempting to be a team that contends for a playoff spot starting next season.
"If I can quote someone from my staff today who has been with us for a few years, 'It's way more fun adding than deleting,' " Dorion said. "We're transitioning. I said at the end of the season that we want to play meaningful games at the end of the year and I think this is one step closer to doing that. Obviously the rebuild has been going on, we feel we're in the next phase now and for us adding a player of this caliber you have to pay a certain price. We felt it was a fair deal."
Dorion said he and Davidson had been working on the details of the trade for a while, but it might have been pushed toward a conclusion during a chance meeting they had at a Montreal restaurant Wednesday night.
"He came over, sat at our table, introduced him to the family," Dorion said. "We were able to step outside and I gave him possible scenarios that could happen, maybe not happen.
"I can tell you Kyle Davidson was great to deal with. A lot of guys you deal with you're not sure you're going to get to a deal. We got to a deal. They are trying to do something we were trying to do a few years ago and now we're trying to do something a lot of teams are trying to do and that's win a lot of hockey games."
Dorion also said the trade got a unanimous thumbs up from everyone on the Senators staff, including assistant general managers, pro scouts, amateur scouts and coaches.
"When we started talking in details about it the last few days there wasn't one person that said, 'Don't want you to make this,' " Dorion said. "It was pretty unanimous in our group that this is the right thing to do in the direction we're going right now."
He also got the approval of Senators forward Brady Tkachuk, their captain, and defenseman Thomas Chabot.
"I had a group chat with both of them; Brady is in Greece right now and Thomas was going to announce our first pick," Dorion said. "I just told them we've added a pretty good player and I got a thumbs up and a heart."
In addition to Tkachuk and Chabot, DeBrincat mentioned Tim Stutzle as someone he is looking forward to playing with.
"I haven't watched him too much but from what I've seen, he seems very skilled," DeBrincat said. "Great with the puck and can move the puck well. I think he's also not afraid to get into the corners and get into battles. From what I've seen, he likes to compete. That's the best team you can have is a guy who's not afraid to mix it up and obviously, there are a couple of guys on this team that are like that, that have the skill to make plays out of the corners."
NHL.com staff writer Tracey Myers contributed to this report