Coughlin interviewed Sheridan and secondary coach Peter Giunta for the coordinator's job Sunday. Giunta was the Rams' defensive coordinator when they won the 2000 Super Bowl.
Sheridan has spent four seasons with the Giants, with his biggest challenge coming in 2007 when he helped Mathias Kiwanuka make the move from defensive end to linebacker.
"As a linebackers coach, you're a central figure in the spoke, because you're involved in the coordination of the front and the linebackers and then the back seven," Coughlin said. "He has done a good job of encompassing the entire defense and grasping the aggressive style."
Before coming to the NFL, Sheridan spent two decades as a college assistant, coaching all the positions on defense in that span.
"Obviously, I'm thrilled," said Sheridan, who'll turn 50 next week. "I'm humbled but very, very excited and anxious to get going. I've prepared my entire career for this opportunity."
The Giants played an aggressive blitzing defense in Spagnuolo's two years as defensive coordinator, and Sheridan said that he will keep the system, although he will make some modifications.
"I'm sure, as much as anything, that's Tom's motivation for promoting from within, whether it was me or Peter Giunta, (was) to keep the defense in place," Sheridan said. "It's obviously a proven, excellent system that Steve brought from Philadelphia.
"You're obviously going to have a slightly different tint to it, because you have a different coordinator and will get different input from whoever Tom brings in from outside to complete the staff," added Sheridan.
The players seem happy with the choice.
"It's good to know that there will not be many changes," middle linebacker Antonio Pierce said. "Bill is a hard worker and is very familiar with the defense. Obviously, we did great things on defense over the last two seasons, and I am looking forward to what Bill will bring as defensive coordinator."
Coughlin now has two coaching vacancies - for a linebackers coach and an assistant offensive line coach.