Eventually Leon Hall’s gut told him to sign with the Giants. But he had to go back to where his heart was to figure it out.

That’s why the veteran cornerback left Wednesday’s visit with the Giants in New Jersey without signing their one-year offer, flew home to Cincinnati where he played for nine seasons to discuss the situation with his family, then flew back to New Jersey on Thursday morning to sign the deal. By the time the team was practicing in late morning, Hall was on the sideline watching in a gray shirt and, perhaps for the first time since his days at Michigan, blue shorts instead of black or orange. He’ll be integrated into the action on Friday.

“Throughout this whole process, there have been a lot of things happening, both good and bad,” Hall told reporters at his introductory news conference. “A lot of various different ways. You can do pros and cons to a lot of situations, but I think that for me personally, a lot of the time I go off my gut and just instincts, if you will, and that’s how I felt about this place.”

After a career with the Bengals, a team that made him a contract offer, he said, and was in need of a veteran cornerback because of injuries, Hall decided to try something new.

“It’s bittersweet,” he said of leaving Cincinnati. “It was a tough decision to make. Obviously, my family is back there, so that’s number one. Like I said, I felt comfortable here and I felt good about where this team is going. I like Coach McAdoo and really what he’s been doing since he got here. Like I said, I just went off my gut instincts and I feel comfortable here.”

He should fit in nicely in a Giants secondary that seems to have plenty of talent on the outside but few clear options in the slot. So far in camp the Giants have used Trevin Wade there and mixed in rookie Eli Apple and Dominique Rodgers-Cromartie. Hall, who has played in the slot throughout his career, will ideally earn that important job.

“We’re fortunate to add Leon to the roster,” Ben McAdoo said in a statement (he did not address the media otherwise on Thursday). “He’s a pro’s pro, has played a lot of football, and has a nice skill set for us . . . We see him playing a lot of inside football for us, serving as a nickel. But never say never when a guy has a chance to move around.”

Defensive coordinator Steve Spagnuolo said he has always liked Hall — the Giants were interested in drafting him in 2007 when he went to the Bengals in the first round in the same class as Darrelle Revis and the Giants eventually selected Aaron Ross — but he took a more wait-and-see approach to how well Hall can adjust after nearly a decade in one city and one team under one head coach, Marvin Lewis.

“I don’t think we should rush to judgment on Leon,” Spagnuolo said. “He’s going to have some things he has to learn and pick up, too. It’s going to all be new and different for him.”

The addition of Hall could squeeze out some younger players. Wade, for one, has been seeing the most reps in the slot. Those opportunities figure to diminish. And Apple, the first-round pick, could have a harder time getting on the field. With Rodgers-Cromartie and Janoris Jenkins as established starters on the outside and Hall in the slot, there won’t be as many opportunities for Apple to get on the field at first.

”Oh, we’ll get him in there,” Spagnuolo said. “There’s a lot of downs in this league now with three wide receivers, four wide receivers, so I don’t anticipate that being a problem.”

There’s no guarantee that Hall will make it through the season, anyway. He’s 31, has had a pair of Achilles injuries in the past four seasons, and is coming off back surgery.

“My back’s feeling good, which is a great feeling,” he said. “It’s been a long road for me since I had my surgery in January. I’ve kind of been quietly going to work and rehabbing every day. Working out for months, so I like where I am right now.”

Not just from a medical perspective, it seems, but a geographic one as well.