New York will now possess the No. 5 and No. 10 overall picks in the first round of the NFL Draft, which begins on April 23rd.
Lawrence, 28, had previously requested a trade from the Giants earlier this month after both sides were at an "impasse" on contract extension talks.
The trade deal will become official if Lawrence passes his physical when he flies to Cincinnati on Sunday.
Lawrence is coming off the worst season of his career after putting up lows across the board with 31 tackles, eight quarterback hits, and 0.5 sacks through all 17 games last year.
He has 341 tackles and 30.5 career sacks through 109 career games. But one of Lawrence's biggest perks is his durability, having played at least 16 games in six of his seven years in the NFL, missing just seven games in total.
The two-time All-Pro defensive tackle has two years left on his contract. He's set to make $18.5 million in base salary ($20 million total) this upcoming season and $17 million total next year before becoming an unrestricted free agent.
The former 17th overall pick in the 2019 NFL Draft has established himself as one of the most dominant interior defensive linemen in the league and will make an immediate impact for any team that steps up and trades for him.
The Giants now have eight draft picks in total (5th, 10th, 37th, 105th, 145th, 186th, 192nd, 193rd).
