The move sends Josh Rosen, who started Miami's past three games, to the bench.
"Kind of came to that conclusion over the last couple of days. We felt like that was the best thing for this team," Flores said Wednesday. "[Fitzpatrick provides] the best opportunity for this team to go into a tough environment and try to pull out a win."
Fitzpatrick, who started Miami's first two games, nearly led the Dolphins to a 14-point fourth-quarter comeback Sunday against Washington after Flores benched Rosen. But Miami (0-5) failed on what would have been the winning two-point conversion and lost 17-16.
Dolphins players said after the game that they had a different energy and level of play with Fitzpatrick.
"We need to be more productive on offense," Flores said. "It's a team game, so players respond to each other and the group. The quarterback has the ball in his hands on every snap. ... Players on every team have to respond to the quarterback."
Flores said following Sunday's loss that Rosen would remain the starter because he provided continuity, but the coach kept the door open for a switch. That move officially came Wednesday after the Dolphins began their practice week.
Flores' decision to demote Rosen seems to be an indication of how Miami feels about the second-year quarterback. Flores said last week that Rosen was "settled" as the quarterback, but he noted Wednesday that Rosen's lack of production and poor play made the coach change his mind after three quarters Sunday and again on Wednesday.
"I'm bummed out. But it's a part of the process. And if Coach wants to make the decision, it's his decision to make," Rosen said. "I wish I would have made it a little tougher on him. But it's a long season. I'm going to continue to push Fitz and be there for him, like he was there for me."
Rosen ranks last among starting quarterbacks in completion percentage, quarterback rating, QBR and yards per attempt. He recorded a Total QBR of 2.1 last week, the second-worst QBR game of the season (behind former New York Jets quarterback Luke Falk in Week 5). His air yards to the sticks was minus-8.9 (meaning he averaged throwing 8.9 yards behind the sticks), per NFL Next Gen Stats. That's the lowest AYTS game for any QB this season with a minimum of 14 attempts.
"We have a lot of confidence in Josh," Flores said. "For him, it's got to be a day-to-day improvement, getting better and continuing his development. That's the conversation I had with him. He's still a young, talented player. There's still a lot of room for development for him. We'll continue to develop him in practice. But at the end of the day, we're looking for production at all positions. We felt like playing Fitz would be in the best interest of the team."
Rosen, a 2018 first-round pick, was traded from the Arizona Cardinals to Miami in April once his former team selected Kyler Murray as its quarterback of the future. Rosen hoped to prove to Miami that he could be the long-term answer at the position.
The Dolphins are strong contenders to be in the market for a quarterback in the 2020 draft, where they have three first-round picks, including the projected first overall selection.
Fitzpatrick, 36, said he had a lot of fun in Sunday's game and noted the team's confidence on the last drive.
Fitzpatrick said this is just another chapter in what he describes as a "roller-coaster" career.
Asked how he can help Rosen deal with the benching, Fitzpatrick said: "I think part of it is just being there. He knows I'm there and he knows I've been through a lot of different things. I wasn't a first-round, high draft pick, but I have been the guy that has been the starter and quote, unquote franchise guy, getting paid money and whatever else. So I've had the weight of the world on my shoulders at times and I know as a quarterback -- and especially as a young guy and a guy that got drafted high -- you feel that pressure sometimes.
"Every Sunday I've got the fate of this whole team on my shoulders, and that's what you do as a quarterback. But if you allow it to overpower you and you allow it to cripple you, then it will. And so part of it is just trying to play free and trying to really hone in on the details of your job and going out there and executing. I'll openly answer questions for him, but I also think at times [it's] just watching; he's a lot more talented than I am, but just watching certain things about me, maybe things he likes or doesn't like and figuring out things that he might want to apply to his game or things he'll try to avoid."
Now Fitzpatrick gets another start against one of his former teams. He played in Buffalo from 2009 to 2012.
"[We're] getting ready for Ryan Fitzpatrick and what he brings to the table -- good quarterback, experienced, brings good energy, can make every throw, gets the ball out," Bills coach Sean McDermott said after hearing that the Dolphins were making the switch. "We have a lot of respect for Ryan."