According to NFL Network's Adam Schefter, the Rams will pay Spagnuolo $11.5 million over four years.
The team said in a press release that Spagnuolo would be introduced at a news conference at noon ET Monday.
"Steve has been on some outstanding defensive staffs during his 10 seasons in the NFL," Devaney added. "He represented what we were looking for when this process began."
"Having a guy whose got swagger makes a difference," Rams linebacker Will Witherspoon said. "A guy who can really get guys motivated is going to be a big key."
After hearing Spagnuolo was leaving to take the St. Louis job, New York defensive tackle Fred Robbins told Giants.com, "He is well-respected by all of us as players. He's more than a coach, it's more than just football with Coach Spags. He's a mentor and takes a personal interest in his players. I wouldn't say he's a players coach, but he knows what it takes to motivate his players. He gets us to work hard, but we have fun doing it and enjoy it, so it makes us want to work even harder."
Added Giants cornerback Corey Webster: "You could see when he first came in here, early on, that he is a stand-up guy. We all had to earn his trust, but once we did, we began to play the aggressive style defense we all love to play. He is an aggressive coach by nature, and that's what makes him fun to play for."
Spagnuolo was one of five finalists for the Rams' job, along with Haslett, Dallas Cowboys offensive coordinator Jason Garrett and defensive coordinators Rex Ryan of the Baltimore Ravens and Leslie Frazier of the Minnesota Vikings. Garrett flew into St. Louis on Friday night, prompting speculation that he would be the Rams' new coach, but he was only in town for another interview.
"He did a great job in his two years with the Giants," Coughlin said. "We've been very, very aggressive on defense, and we've been able to have two very successful years back-to-back. Steve has made an outstanding contribution to our team, and we wish Steve and Maria (his wife) all the best."
Last season, the Giants upset the favored Cowboys and Green Bay Packers to reach the Super Bowl against New England, with the Patriots seeking to become the first 19-0 team in NFL history. But Spagnuolo's defense harassed New England quarterback Tom Brady all day, sacking him a season-high five times, and held down the Patriots' potent offense in a 17-14 upset victory.
Despite New York's loss to the Philadelphia Eagles in the NFC divisional round this season, many considered this an even greater coaching job by Spagnuolo after seven-time Pro Bowl pick Michael Strahan retired last summer and fellow Pro Bowl defensive end Osi Umenyiora was lost during the preseason with a major knee injury.
New York ranked fifth in the league in total defense, giving up 294 yards per game. That's a far cry better than the Rams, who ranked 28th at 465 yards per game.
Spagnuolo faces a big challenge with the Rams, who won their first two games after Haslett took over, then lost their final 10.
St. Louis is 5-27 over the past two seasons, hasn't had a winning season since 2003 and hasn't made the playoffs since the 2004 season. The Rams' offense was even worse than the defense last season, tying for 30th in scoring offense at just 14.5 points per game.
On the plus side, St. Louis will have the second overall pick in the draft for the second straight season. The Rams have a top-tier running back in Steven Jackson and some promising young players, including defensive end Chris Long, the No. 2 overall pick in 2008, and speedy wide receiver Donnie Avery, a second-round draft pick last year.
Spagnuolo, a Massachusetts native, was a wide receiver at Springfield (Mass.) College, and he got his first taste of the NFL as a player personnel intern with the Redskins in 1983. After several other stops at the college and pro levels, Spagnuolo was hired as the Frankfurt Galaxy's defensive coordinator in 1998. He was hired the following year by the Eagles and worked his way up from defensive assistant to coordinator.
Information from The Associated Press was used in this story.