The Giants got their tight end. It just wasn’t either of the ones anyone thought they would get.

Evan Engram, the 6-3, 234-pounder from Mississippi, was taken by the Giants with the 23rd selection in the first round of the NFL Draft on Thursday night. The Giants had been looking at tight ends throughout the predraft process and seemed to be focusing on O.J. Howard and David Njoku. Howard went to the Bucs four picks ahead of the Giants’ selection. Njoku remained on the board and eventually landed in Cleveland with the 29th overall pick.

Ben McAdoo said the Giants had “limited” contact with Engram during the last few weeks and months. There were no visits, no workouts. Even Engram seemed surprised. A bit.

“It came out of nowhere,” Engram said. “But I always felt they had their eye on me . . . I dreamed of playing for a couple of teams, I had a couple in my mind, and New York was at the top.”

Engram is an athletic, pass-catching tight end who will essentially be teamed up with blocker and free agent acquisition Rhett Ellison to combine and create a full tight end. Engram gives the Giants a burst of speed from that position like they have not seen in many years — he ran a 4.42 40 at the NFL Combine — and is more like a wide receiver that a traditional in-line player.

He is the latest addition to the offense this offseason. Besides Ellison the Giants also added receiver Brandon Marshall early in free agency. The expectation is that those additions will be able to spark an offense that was unexpectedly moribund in 2016, having never scored 30 points in any single game.

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“We think this guy can be a dynamic weapon in our offense,” general manager Jerry Reese said. “We think he can be a matchup nightmare for teams trying to cover him with linebackers and safeties.”

“The Giants have been missing a piece like me,” Engram said, noting that he had been watching Giants games last year. “I felt I could be another more dynamic piece in that role . . . I know for a fact I’m ready to come in and make an immediate impact.”

Engram is the first tight end selected by the Giants in the first round since Jeremy Shockey in 2002. But the Giants see him as much more than that.

“We’re calling him a tight end, calling him an H-back,” Reese said. “Call him whatever you want to call him. We see him as a guy who can line up at any of the receiver positions, tight end, in the slot. He can line up anywhere.”

“The speed and the yards after catch just jumps out at you when you put on the tape,” McAdoo said.

As for helping the offense score, McAdoo noted that “the fastest way to the end zone is right down the middle.”

The Giants have not had a player to exploit that route in some time.

For a while it seemed as if the entire Giants board might be falling to them. That ended with Howard and the Bucs connecting with the 19th pick. At 20 the Broncos selected Garett Bolles from Utah, the first offensive lineman selected. Linebacker Jarrad Davis went at 21 to the Lions. The Giants had an eye on all three of those with the 23rd pick.

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“We thought guys would come off the board all over the place and it did that,” Reese said. “I don’t think anybody was surprised by anything that happened.”

Engram said he has spent time with Eli Manning, a fellow Mississippi product, over the years, and has even caught a few passes from the Giants quarterback when both found themselves on the Ole Miss campus.

“I can’t wait to play with him and learn from him and be a great player for this team,” Engram said.

Reese compared Engram to Washington’s Jordan Reed. The Giants were the only team in the NFC East without such a weapon at tight end. Now they have one, too.

“He’s hard to handle,” Reese said. “We think that’s a tremendous weapon for our offense. We’re just trying to help the offense any way we can and help the team anyway we can.”

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GIANTS PICK UP BECKHAM OPTION. Meanwhile, the Giants made a move with their first-round pick from 2014 and picked up the fifth-year option on Odell Beckham Jr.’s contract. The maneuver was expected and reported last week, but the team made it official on Thursday.

The fifth-year option will pay Beckham roughly $8 million for the 2018 season. Because he was selected outside the top 10 picks of his draft class, Beckham’s option salary is calculated as the average of the third through 25th-highest paid players at his position. Beckham’s base salary for 2017 is just over $1.8 million.

In each of this first three seasons with the Giants Beckham has led the Giants in receptions, receiving yards and touchdown catches, and was selected to the Pro Bowl. He is the first Giants player to make the Pro Bowl in each of his first three seasons since Lawrence Taylor from 1981-83.