NFL

Giants land Shane Vereen after Patriots opt not to match offer

Injuries, large and small, forced the Giants to scour the scrap heap the past two seasons to sign healthy bodies when their running backs started getting hurt. They took a step Tuesday toward fixing that problem as NFL free agency got underway with a move that not only bolsters the offensive backfield, but also adds a skill set they previously did not possess.

The agreement with Shane Vereen on a three-year, $12.35 million contract (with $4.75 guaranteed) allows the Giants to take a piece from the Super Bowl champion Patriots.

“I’m very excited,’’ Vereen told The Post. “Very excited.’’

On a busy opening day, the Giants came to terms with five players, including another New England player, linebacker Jonathan Casillas. They also added Cowboys return ace Dwayne Harris, former Packer and Bengal right tackle Marshall Newhouse and former Bears and Jaguars linebacker J.T. Thomas.

The new contracts total $55.6 million, however, none but Harris, a return man, is likely to crack the starting lineup, at least initially.

Last month, Giants general manager Jerry Reese admitted it still “stings a little bit’’ to have lost David Wilson to premature retirement, given the skill set Reese loved in Wilson when he made him a first-round draft pick in 2012.

“We will try to replace that position,’’ Reese said.

The replacement is Vereen, as the Giants were determined to add a running back with some speed and pass-catching ability to complement what Reese calls “some big bangers’’ already on the roster, Rashad Jennings and Andre Williams. Anyone who saw what Vereen brought to the table in Super Bowl XLIX knows he’s got something the Giants did not previously possess.

Vereen was targeted 12 times and caught 11 of Tom Brady’s passes for 64 yards to keep the chains moving against the Seahawks. In the past two seasons, Vereen amassed 99 receptions for 874 receiving yards and six touchdowns. He figures to complement the pounding styles of Jennings and Williams. It is believed Vereen gave the Patriots the chance to match an offer from the Giants.

Coach Tom Coughlin always insists there is room and a need for three running backs within the offense. Remember the “Earth, Wind and Fire’’ three-headed running-back monster that in 2008 led the league in rushing?

Jennings, signed a year ago, played in only 10 games in his first season with the Giants, beset by knee and then ankle injuries, finishing with 167 rushing attempts and 639 yards. Williams, forced at times to carry the load as a rookie, struggled early and later showed improvement as he led the team in rushing attempts (217), rushing yards (721) and rushing touchdowns (seven).

In his four years with the Patriots, Vereen, 26, never emerged as a workhorse back after arriving as a 2011 second-round pick out of California. Of course, the Patriots are all about interchanging their running backs, and Vereen certainly developed a specialty role. He has seven career receiving touchdowns and in 2014 had career highs in rushing attempts (96) and rushing yards (391). His career average is 4.2 yards per rushing attempt.

Vereen (5-foot-10, 205 pounds) does not have the bulk of Jennings and Williams — who pack a punch at 230 pounds apiece — and thus adds a different dimension to Ben McAdoo’s offense. His addition can also be seen as a boon to the receiving corps. Vereen is not merely a swing-pass type of target; he can line up as a receiver and go get the ball down the field, something few running backs ever master.

Five Giants running backs in 2014 combined for 62 receptions, led by Jennings (30) and Williams (18). Vereen had 52 catches last season for the Patriots.

In addition to Jennings and Williams, the Giants also have Orleans Darkwa, Michael Cox and Chris Ogbonnaya (who was re-signed Tuesday) on the roster at running back.