The team said in a release that Spagnuolo would be introduced at a news conference at 11 a.m. CST Monday.
"We considered some very qualified and outstanding candidates for this position, but we kept coming back to Steve Spagnuolo," general manager Billy Devaney said in a statement.
The St. Louis Post-Dispatch was the first to report the hiring and said Spagnuolo would be paid just under $12 million.
Spagnuolo replaces Jim Haslett and takes over a team that finished 2-14. Haslett went 2-10 as interim coach after his promotion from defensive coordinator when Scott Linehan was fired following an 0-4 start.
"Billy did a spectacular job of presenting some fabulous candidates," owner Chip Rosenbloom said in a statement. "We're very excited that Steve will be our head coach and are looking forward to an exciting season."
Spagnuolo was the architect of the Giants' sack-happy defense that thwarted New England's run to a perfect season in last year's Super Bowl upset. Devaney was impressed with Spagnuolo's no-nonsense demeanor during an interview in Los Angeles on Thursday.
"There's just a toughness about him," Devaney said. "He represented what we were looking for when this process began."
"Having a guy who's got swagger makes a difference," Rams linebacker Will Witherspoon added. "A guy who can really get guys motivated is going to be a big key."
Spagnuolo was one of five finalists for the job, along with Haslett, Dallas offensive coordinator Jason Garrett and defensive coordinators Rex Ryan of Baltimore and Leslie Frazier of Minnesota. Garrett flew into St. Louis on Friday night, prompting speculation he would be the new coach. But he was only here for another interview and perhaps as a backup option in case Spagnuolo was hired elsewhere.
"It wasn't a make or break deal," Devaney said. "Jason was a very strong candidate."
The 49-year-old Spagnuolo took over as defensive coordinator in New York in 2007. A year before, New York ranked 25th in total defense. Under Spagnuolo in 2007, the Giants ranked seventh, led the league with 53 sacks and made the playoffs.
"I'm very happy for Steve," coach Tom Coughlin said. "We've been very, very aggressive on defense and we've been able to have two very successful years back to back."
Last season, they upset favored Dallas and Green Bay to reach the Super Bowl against New England with the Patriots seeking to become the first 19-0 team. But Spagnuolo's defense harassed Tom Brady all day, sacking him a season-high five times and holding down New England's potent offense in a 17-14 upset win.
"Of course being a defensive guy you'd like to have a defensive guy in charge," Witherspoon said. "No matter what, they want to make every game close. They want to make every situation a win-win situation."
Despite New York's loss to Philadelphia in the NFC divisional round this season, many considered this an even greater coaching job by Spagnuolo after seven-time Pro Bowler Michael Strahan retired last summer and fellow Pro Bowl defensive end Osi Umenyiora was lost in 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, giving up 465 yards per game.
The day after the Giants were knocked out of the playoffs, New York defensive end Justin Tuck described Spagnuolo as "one of those coaches where he can kind of yell at the star player and get away with it because everybody loves him that much."
"I wouldn't say he's a player's coach, but he knows what it takes to motivate his players," cornerback Corey Webster said. "He gets us to work hard, but we have fun doing that and enjoy it, so it makes us want to work even harder."
Spagnuolo interviewed for several other head coaching vacancies each of the past two seasons. He was a strong contender last season for the top job in Washington before deciding to stay with the Giants.
He faces a big challenge in 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 offense was even worse than the defense last season, tying for 30th in scoring offense, averaging just 14.5 points per game.
On the plus side, St. Louis will have the second 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 second-round draft pick Donnie Avery, a speedy receiver.
Spagnuolo, a Massachusetts native, was a wide receiver at Springfield (Mass.) College. He got his first taste of the NFL as a player personnel intern with Washington 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 Philadelphia and worked his way up from defensive assistant to coordinator.