The Athletic's Jason Butt first reported the news.
The Dolphins selected Harris 22nd overall in 2017, but he struggled to break into the defensive line rotation, making just eight starts in 41 games played.
He showed promise during his rookie season with 12 quarterback hits, five tackles for loss and two sacks. But the Missouri product has managed just 11 quarterback hits, five tackles for loss and 1.5 sacks in 25 games over the past two seasons combined.
Harris is set to earn $1.94 million next season in the final guaranteed year of his rookie contract, per Spotrac.
The Dolphins have spent this offseason reshaping their roster, as Kyle Van Noy, Emmanuel Ogbah and Shaq Lawson were brought in to upgrade the pass rush.
Atlanta, meanwhile, had an opening on the defensive line after letting Vic Beasley leave in free agency. Harris will likely play behind Dante Fowler Jr., who signed a three-year, $48 million deal in March.
The Falcons' 28 sacks in 2019 ranked 29th overall and marked their lowest total since 2014 (22).