The Giants on Monday announced they had signed Smith and cornerback Valentino Blake, who also excels on special teams. A second-round draft choice out of West Virginia in 2013, Smith has been a bust after a good rookie season. He missed most of last season after surgery for an ACL injury in October.
"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 believes he can learn from Manning, a two-time Super Bowl MVP, and develop under coach Ben McAdoo and quarterbacks coach Frank Cignetti.
"I think it will work out tremendously for me," Smith said. "And it's also an opportunity to be on a real good team, a winning team, get healthy - it's just a perfect scenario for me. I couldn't have written it up any better myself."
The Giants signed backup Josh Johnson last week. Ryan Nassib is a free agent.
Smith has hit 501 of 866 pass attempts for 5,962 yards, 28 touchdowns and 36 interceptions. The 26-year-old has a 12-18 record as a starter.
Being the Giants' backup means not getting a lot of play. Manning has started 211 consecutive games since 2004.
"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," Smith said. "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."
Blake, 5-9 and 198 pounds, entered the NFL with Jacksonville in 2012 and has also played Pittsburgh and Tennessee. He has played in 78 regular-season games with 18 starts. He has 148 tackles, three interceptions, a sack and 27 passes defensed, plus 38 special teams tackles.
The Giants have signed former Jets receiver Brandon Marshall, tight end Rhett Ellison and offensive lineman D.J. Fluker. They also re-signed defensive end Jason Pierre-Paul, guard John Jerry, long snapper Zak DeOssie, and Johnson.