The Giants’ recycling program continues.

The team agreed to terms with veteran defensive tackle Barry Cofield on Wednesday, according to his agent, adding him to a long list of former Giants who have come home to the franchise after spending time elsewhere. On this current roster alone he joins Hakeem Nicks in that category, and in recent history others such as Brandon Jacobs, Chase Blackburn, Aaron Ross and Mario Manningham have also had second go-rounds with Big Blue.

Cofield was traveling to the Giants on Wednesday night to sign his contract. To make room, the Giants cut veteran safety Brandon Meriweather. The Giants signed him late in training camp to help their depleted secondary, but his performance dwindled throughout the season and he was sidelined the last two games by a knee injury.

The Giants needed another defensive lineman with the recent injury to Markus Kuhn, who hurt his knee against the Dolphins, and George Selvie in the concussion protocol. The Giants have already lost their best interior defensive lineman, Johnathan Hankins, for the season.

Cofield worked out for the Giants several weeks ago and they kept him on a short list. Jason Pierre-Paul, the only defender on the Giants who was a teammate of Cofield’s, said the veteran looked good and healthy when they spoke at that time.

“He’s a well-respected player and has done it for a long time,” said Cullen Jenkins, who never played with Cofield. “I look forward to him being here.”

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Cofield was a fourth-round pick of the Giants in 2006 and played five seasons for the team, starting all but two games in that span. He started all 16 games each season from 2011-13 for Washington, where he signed as a free agent, but last year appeared in just eight games with three starts dealing with a variety of injuries including a high ankle sprain as well as abdominal and groin muscle issues. He was on short-term injured reserve in 2014 and was released in the offseason.

Meriweather’s release leaves the Giants with three safeties: Landon Collins, Craig Dahl and Cooper Taylor. Taylor was waived by the team in midseason but re-signed a few weeks later to the practice squad before returning to the active roster. He played well Sunday against the Dolphins, which may have boosted the team’s confidence in him and helped make the decision on Meriweather.