Giants coach Joe Judge confirmed that Hill had been traded and the Bengals announced they acquired Hill for Price, the 21st pick overall in the 2018 draft.
The deal for players entering their fourth seasons comes just a day before NFL teams have to cut their rosters to the 53-man limit for the regular season. Neither player was projected to be a starter this season.
A former star at Ohio State, Price has not lived up to expectations in the NFL. Trey Hopkins has taken over at center.
Price, who had one start last season, wasn’t expected to see much action. He started the 10 games in which he played as a rookie, but only nine in the past two seasons.
Hill was a third-round draft pick for the Giants out of North Carolina State. He played in all 48 games with 17 starts over the past three seasons and had 7 1/2 sacks, 13 quarterback hits, 10 tackles for loss and three passes defensed.
Hill did not play in the Giants’ 22-20 loss to the Patriots in the preseason finale because of the impending trade, Judge said.
“It’s a position where, honestly, he’s drawn a lot of interest,” Judge said. “I have a lot of respect for B.J. as a player. I think he is a starting defensive lineman in this league.”
The Giants’ offensive line was a question mark heading into the season and it struggled on Sunday night against New England in its final dress rehearsal for the season opener against Denver on Sept. 12.
Left tackle Andrew Thomas whiffed on at least three blocks, two of which led to Daniel Jones being either sacked or hit.
Left guard Shane Lemieux has not played in a preseason game because of a knee injury early in camp. Nick Gates is solid at center, but the right side of the line is a question mark. Guard Will Hernandez is making the move to the right side after losing his job to Lemieux last season.
Veteran Nate Solder and second-year pro Matt Peart are vying for the right tackle spot. Neither has been overly impressive.
The Giants have long used their offensive linemen in a number of roles so Price probably will be used at both center and guard to test his versatility.