The Giants were set to sign Stokley even after getting good news about Hakeem Nicks, who said Wednesday that his knee injury was just a bone bruise.
"I don't see myself missing any time," said Nicks, who caught seven passes for 122 yards but was injured on a deep pass during Sunday's 28-14 loss at Washington.
Stokley played 11 games for the Seattle Seahawks last season, his 12th in the NFL, and caught 31 passes for 354 yards.
The 35-year-old wideout was once a reliable target for Peyton Manning in Indianapolis, where he spent four seasons. In his best season, he caught 68 passes for 1,077 yards and 10 touchdowns in 2004.
Stokley signed with the Seahawks last season after reaching a settlement with the Denver Broncos that made him a free agent.
He has also played for the Baltimore Ravens and has 338 career receptions for 4,673 yards and 34 touchdowns.
The Giants have been weakened by injuries, especially on defense, but Hicks said he was never really worried about his knee, which he also hyperextended.
"I looked at it like I finished the game ... knowing it wasn't that serious," said Hicks. "I think when you start worrying, that's when stuff is wrong so I was just trying to keep a cool head the whole time. Everything came back good so that is a blessing."