The signing was confirmed by a team official.
Considered one of the NFL's best nickel cornerbacks, Dockery can become an unrestricted free agent next spring absent a contract extension or the team's use of a transition or franchise tag on him.
By virtue of the one-year tender in February, New York retained a right of first refusal on Dockery's services. The club tendered Dockery at the second-round level, meaning it would have received a second-round draft choice if Dockery signed an offer sheet with another team and the Giants opted not to match it.
The deadline for signing restricted free agents to offer sheets is April 17. After that, their exclusive rights return to their current team.
A former Mississippi State standout, Dockery entered the league in 2006 as an undrafted college free agent. Although undersized at only 5-foot-8, Dockery is a very physical player and solid tackler.
Dockery, 25, has appeared in 40 games, with seven starts. Six of those starts came in 2007. He has 124 tackles, three interceptions, and 22 passes defensed. Dockery had two interceptions last season.
Senior writer Len Pasquarelli covers the NFL for ESPN.com.