Atkins agreed to a four-year extension worth $65.3 million, according to Adam Schefter of ESPN, who also reported that Dunlap has agreed to a three-year, $45 million extension.
Atkins' current contract was set to expire in 2019, but now he is under contract through the 2022 season.
He has been named to the Pro Bowl six of the past seven years and was a first-team All-Pro in 2012 and 2015. The 30-year-old Atkins has accumulated 61 sacks in eight NFL seasons, and he had nine sacks each of his last two seasons. He also had 2.5 sacks in four postseason games.
Dunlap was heading into the final year of his contract, and he was scheduled to make $7 million in base salary this season.
The 29-year-old Dunlap has been named to the Pro Bowl twice (2015, 2016), and he has recorded 64.5 sacks in his eight pro seasons. His best season came in 2015 when he had 13.5 sacks, and he followed that with eight sacks in 2016 and 7.5 sacks last year.
Dunlap has started all 16 games each of the last four years.
For at least two more seasons, the Bengals have Atkins, Dunlap, defensive end Carl Lawson, defensive end Jordan Willis and defensive end Sam Hubbard under contract.