Here is what Jabrill Peppers wants Giants fans to know about him after completing his first two NFL seasons with the Browns: He can be a whole lot better.

“Me personally, I feel as though I haven’t even showed a third of what I can really do,’’ Peppers said Monday after he and Odell Beckham Jr. passed their physical exams, stamping as official the mega-trade between the Giants and Browns. “So, I’m anxious just to get there and have a fresh beginning, and immerse myself in the culture and tradition, learn the schemes and be the best player I can be.”

In addition to Peppers, 23, the Giants brought back a 2019 first-round pick (No. 17 overall) and a third-round pick (No. 95 overall). And so, Peppers is only a piece of the bounty the Giants got back, and that could lead to added pressure to perform.

“I didn’t trade Odell straight up for Jabrill Peppers,’’ general manager Dave Gettleman said. “Jabrill was an important piece to that trade. I’ve said it before and I’ll say it again, I believe in his ability.’’

Peppers had every right to believe he was part of the big doings in Cleveland, part of a franchise resurgence. Just like that, he was shipped out.

“It’s a business, so nothing really can surprise you,’’ he said. “It’s just more of a blessing in disguise and I feel as though God doesn’t make mistakes. It was more of an exciting, exhilarating feeling. Just a new road to go down, and I’m excited to go down it.”

This is a homecoming for Peppers. He is from East Orange, N.J., and won four state high school championships, two apiece at Don Bosco Prep and Paramus Catholic. Peppers said his family is excited to have him back home.

“It’s a much easier commute than Cleveland, Ohio,’’ he said. “So, that works out.”

Gettleman said he was not ready to trade Landon Collins at the deadline last season. He scoffed at a report the Giants were offered a first-round pick for Collins; the actual offer, The Post previously reported, was a fourth-round pick.

“Did we have teams call on Landon? Yes,’’ Gettleman said. “But at that point in time, it wasn’t what I thought he was worth, and at that point in time we were really struggling and what is the message we are sending by trading him? And I didn’t think the value was there. That’s why I didn’t do it.’’

Guard Kevin Zeitler signed a five-year, $60 million contract with the Browns in 2017 and endured an 0-16 season. Zeitler’s second year in Cleveland was much, much better — 7-8-1 — and with the Browns on the rise, Zeitler last week was traded to the Giants as part of the huge trade that sent Beckham and Olivier Vernon to the Browns.

“Once you sign that contract you think you are going to be there for quote, unquote five years,’’ Zeitler said. “It definitely came as a big surprise, but it is what it is. I’m excited and I thank Cleveland for the opportunity. I’m excited to be a New York Giant and I’m ready to get to work.’’

Zeitler, a seven-year veteran, will be the Giants’ starting right guard. He almost sounded wistful when reviewing all the moves made by the Browns this off-season.

“You look at what they have done these past couple of weeks, it’s definitely an exciting time in Cleveland,’’ Zeitler said. “I think the guys there are going to have a very good time this next year. Like I said, there’s nothing I can do about it. They traded and the Giants wanted me. I’m excited to be here and we are going to do everything we can to get the same amount of buzz in New York.’’