EAST RUTHERFORD, N.J. ? Tom Coughlin didn’t say no to the New York Giants this time around, signing to coach them Tuesday.

The former Jacksonville Jaguars coach signed a four-year contract, vowing to bring back a brand of smashmouth, mistake-free football that led New York to two Super Bowls under his mentor, Bill Parcells.

“It is a tremendous challenge, and I am looking forward to working with these players and re-establishing the New York Giants’ tradition of physically controlling the line of scrimmage,” Coughlin said. “We want to win the battle at the line of scrimmage, eliminate the disease of turnovers and control field position of special teams.”

Coughlin and the Giants finalized the deal worth around $12 million Tuesday, a day after Coughlin held his second round of meetings with the team.

Coughlin, 57, succeeds Jim Fassel, who was fired following a 4-12 season in which the Giants lost their final eight games.

“Tom Coughlin is the man we wanted 11 years ago, and he is the man we wanted now,” general manager Ernie Accorsi said. “Aside from his family, Tom has one interest: winning.”

John Mara, the Giants’ executive vice president, called Coughlin “the right person for this job.”

“Our objective at that point was to make sure we hired the right man for this job, and that is what Tom is,” Mara said. “He has experience as a successful head coach at the college and NFL levels, and he is going to bring an intensity and focus and a commitment to winning that we need and want. We stayed true to a process that we felt would produce the kind of head coach we need, and it did.”

A former Giants assistant under Parcells, Coughlin was 72-64 in eight seasons with the Jaguars.