Roper will coach the No. 24 Blue Devils offense in Tuesday's Chick-fil-A Bowl against No. 21 Texas A&M.
Contract details were not immediately known, though the Gainesville Sun reported he will make $600,000 a year.
Florida head coach Will Muschamp expects Roper, his third offensive coordinator in four seasons, to bring new elements to the pro-style offense run by the Gators since Urban Meyer resigned.
"I'm excited to have Coach Roper join our staff," Muschamp said in a statement. "He has a diverse, up-tempo background on offense and does a good job of adapting to what the players do best. The most important thing, though, is he has always remained balanced."
Roper had served as Duke's offensive coordinator, assistant head coach and quarterbacks coach. He was a finalist for the Broyles Award, which recognizes the nation's top assistant coach.
"I feel like this was the right situation for me and my family at the right time," Roper said on a conference call Thursday with reporters. "It's obviously a great university that has a great tradition, and I look forward to trying to add to that.
"Obviously, the expectations are great. I understand that going in, and the challenge is to meet those expectations. We're at the University of Florida, which obviously has a great tradition and has met those expectations a lot in the past. I'm just looking forward to it."
Muschamp brought Charlie Weis from the Kansas City Chiefs to be his first offensive coordinator. Weis left to be head coach at Kansas one year later. Muschamp turned to then-Boise State offensive coordinator Brent Pease, who was fired nearly a month ago.
The Gators offense has struggled mightily in all three of Muschamp's seasons, never ranking above 103rd out of 123 Football Bowl Subdivision teams in total offense.
Florida (4-8) ranked last in the SEC this season in total offense (316.7 yards per game) and scoring (18.8). It was the first time since 1979 that the Gators suffered a losing season and the first time in 22 years that they failed to make a bowl game.
The Gators scored 30 or more points just twice during the 2013 season, tying for 112th nationally in scoring offense. The Gators ranked 113th nationally in total offense.
Roper inherits an offense that features mobile quarterback Jeff Driskel and plenty of running back depth, but also includes a woeful offensive line and few playmakers on the perimeter.
"I think the biggest thing is you got to find out the strengths of your quarterback and the strengths of your offensive line," Roper said. "Once you find those strengths, then you can start putting together what you're going to start hanging your hat on offensively. Then the other five players you have to find out who can make something happen with the football.
"I think there's a reason for tempo in games that obviously causes defenses problems, but we'll never sacrifice tempo over execution. We want to play fast, but we want to play smart and take care of the football and those types of things."
Roper has served as Duke's offensive coordinator since 2008. This year, the Blue Devils ranked 68th nationally in total offense, averaging 408.1 yards per game and 31.6 points per game.
He has extensive history in the SEC. He got his start at Tennessee while serving as a graduate assistant from 1996 to 1998 and then followed current Duke head coach David Cutcliffe to Ole Miss, where he spent six years coaching quarterbacks -- including Eli Manning -- and was the passing game coordinator during his final three seasons.
Cutcliffe said Roper's coaching style includes "intensity, tempo and quality of repetition."
"From the minute they hit the field, it's going to be intense," Cutcliffe said. "I wouldn't call him a laid-back football coach by any stretch of the imagination. It's going to be what we call, treat the ground like a hot stove. If you hit the ground, you better get up running. And you know by the time they get on the field until they get off, they're going to be moving and getting a bunch of quality reps so I would call it very intense."
In 2005, Roper served as Kentucky's quarterbacks coach before serving as running backs coach at Tennessee in 2006 and 2007.
Florida is expected to run more of a spread offense with more tempo under Roper, according to sources.
Edward Aschoff and Jeff Barlis of ESPN.com and The Associated Press contributed to this report.