A South Florida native, the 23-year-old Brinson was the key piece in the deal that sent Christian Yelich to Milwaukee.
He will start in center field and hit leadoff when Miami opens its season on Thursday against the Chicago Cubs.
"It's going to be an emotional day, I think, for me and my parents and everybody that's kind of been with me through the ride, and everybody that saw me play Little League and grow up loving the Marlins," Brinson said. "I just wanted to play in the big leagues, but to get the opportunity to play in the big leagues for the Marlins, that's going to be pretty awesome."
"It's everyone's dream," Cooper said. "Your big league debut's your No. 1 dream and making the opening day roster is another one."
Starlin Castro, also acquired in the Stanton deal, will begin the season as the Marlins' starting second baseman.
Manager Don Mattingly stopped short of releasing the entire 25-man Opening Day roster in part because it remains in flux, especially where the starting rotation is concerned.
Justin Nicolino appeared to be in contention for one of the final rotation spots or perhaps a long relief role, but Miami designated the lefty for assignment and Cincinnati claimed him on Sunday.
"We didn't feel like he was going to be one of our 25," Mattingly said.
The Nicolino move could open a roster spot for Jacob Turner, who allowed four runs in two innings of relief in Sunday's 6-2 loss to Houston. Miami also plans to start minor leaguer Dillon Peters, once a candidate for the rotation, in Tuesday's exhibition against the University of Miami.
Meanwhile, injured starting pitcher Wei-Yin Chen continued to make strides toward proving his elbow is healthy by throwing a 16-pitch live batting practice on Sunday.
Chen is among the injured Marlins who will remain Jupiter to play with minor leaguers, but his rehab is finally showing signs of progress.
"At this point I'm optimistic," Mattingly said. "You feel like you've got a pretty good chance if things stay on this track to get Wei-Yin back this year -- and fairly quickly."
Miami concluded spring with a 15-13-3 record, placing the Marlins in the top half of the Grapefruit League standings.
"I don't really look at wins and losses in camp, but I think for our club it was probably more important that we win some games just because of the predictions of how bad we were going to be," Mattingly said.