The New York Giants have signed veteran cornerback Leon Hall.

The deal is for one year and worth up to $2 million, a source told ESPN's Adam Schefter. Hall, 31, visited the Giants for a second time Wednesday. They wanted another look at his back after his offseason surgery.

Hall impressed during his workout, and was choosing between the Giants and the Cincinnati Bengals. Hall said the Bengals, who drafted him in 2007, also made an offer.

"You can do pros and cons to a lot of situations, but I think that, for me personally, a lot of times, I go off my guts and instincts, if you will," Hall said. "That is kind of how I felt about [the Giants]."

The Giants play the Bengals on a Monday night at MetLife Stadium on Nov. 14.

"One of my friends had texted me about a game in November," Hall said. "It's definitely something I'll be looking forward to. There's no doubt about that."

Hall is expected to compete immediately as the Giants' slot cornerback. Trevin Wade has been running with their first-team defense this summer at that position.

But defensive coordinator Steve Spagnuolo may have bigger plans in mind.

"He's a versatile guy," Spagnuolo said. "He's an experienced vet. I think he can bring some things to the package that we can do to make us do some multiple things that maybe we didn't have a chance to do until this point. So I'm excited about it."

The Bengals' first-round pick in 2007, Hall has started 121 games. He's been used primarily as a slot cornerback the past few seasons.

Spagnuolo said Hall will be used "inside to begin with" in the Giants' defense.

Injuries marred much of the latter years of Hall's time in Cincinnati. He tore both of his Achilles tendons in separate incidents during the 2011 and '13 seasons. Although he returned remarkably strong after the first tear, he has been a little slower getting back to form since the second one. Neither Hall nor his Bengals coaches would say whether he had lost a step after the second injury, but his role was scaled back.

Hall played strictly at the slot corner position in 2015 after splitting more time there and on the boundary at earlier times in his career. He had surgery on his back in January.

"The back is feeling good, which is a great feeling," he said. "I've kind of just been quietly going to work and rehabbing every day, working out. So I'm feeling good. I like where I'm at right now."

Hall believes he can step right onto the field and practice. He's been back at full strength since April or May.

In a corresponding move, the Giants waived cornerback Tramain Jacobs.

ESPN Bengals reporter Coley Harvey contributed to this report.