Geno Smith is officially a Giant. But he knows there is a big difference between being on the team and being on the field.

The former Jet will back up Eli Manning, who has started 199 consecutive regular-season games and is coming off a season in which he threw every pass attempted by the Giants. So if Smith had been looking for a place to play and compete as a free agent, he would not have signed with them.

At this point in his career, though, he’s looking for a chance to reset and learn.

Speaking of Manning’s streak and snap counts, Smith said: “We expect that to continue. I’m not coming aboard expecting anything else. This is definitely an opportunity for me to learn and to get better. I want to carry my notepad around, and whatever I see Eli doing, whether it’s in the classroom, on the field or off the field, I want to write it down. Because he’s a guy you can model yourself after. If you learn from a guy like that, we can all do a lot better.”

Smith had a physical Monday and, according to sources, then signed a one-year, $2-million deal. He agreed to terms with the Giants last week.

“Geno has a great, positive attitude, and he’s looking forward to learning and competing in our QB room,” general manager Jerry Reese said. Smith, 26, is expected to compete for the backup job with Josh Johnson, 30, whom the Giants signed to a two-year deal last week.

In four years with the Jets, Smith threw 28 touchdown passes and 36 interceptions in 33 games. He missed most of the last two seasons because of injuries, including the ACL he tore in his only start last season.

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“Right now, it’s doing great,” he said of his knee. “We’re being cautious. But I’m at that stage where I’m feeling healthy enough that I can push it. But I have to be smart about it and not do anything that will cause me setbacks.”

Why would he need to? Smith’s role in 2017 will be more about growth than playing time. At the end of the season, he’ll again be a free agent. Perhaps he’ll even remain with the Giants as a candidate to eventually replace Manning, 36, who has three years left on his contract.

“I have tons of good football ahead,” Smith said. “I just look forward to this year and having an opportunity to get healthy and learn and become a better quarterback. It’s just a perfect scenario for me. I couldn’t have written it up any better myself.”

Notes & quotes: The Giants signed former Jaguars, Steelers and Titans cornerback Valentino Blake and agreed to terms with linebacker Keenan Robinson, according to NFL Network. Robinson, who visited the Bengals and Bills in free agency, had 83 tackles for the Giants in 2016. They also re-signed linebacker Mark Herzlich.

With Kimberley A. Martin