Dyson, released by Seattle earlier this month in a cost-cutting move, is coming off a Super Bowl appearance in his only season with the Seahawks. The 5-foot-10, 183-pound Dyson spent four years with Tennessee after the Titans selected him in the second round, 60th overall, in the 2001 draft.
He has 17 interceptions and five touchdowns in 72 regular-season games.
"Andre is a good young player who has extensive playing experience at the highest levels in the NFL," Jets general manager Mike Tannenbaum said. "One of our priorities heading into the offseason was to acquire a cornerback that had valuable playing experience.
"He has played in two championship games and a Super Bowl, and that experience will be an asset to the Jets," Tannenbaum said.
Terms of the deal were not released.
Law was released after one Pro Bowl season in New York because it would have been too expensive for the Jets to keep him. That left the Jets with David Barrett as their only experienced cornerback, though Justin Miller started games as a rookie last season because of injuries.
Dyson, a five-year veteran from Utah, started seven games for Seattle last season -- including the Super Bowl loss to Pittsburgh. He missed six games with a strained right hamstring and then a sprained left ankle after sitting out only two games the previous four years.
In Seattle's 42-0 rout at Philadelphia last Dec. 5, Dyson scored after an interception and a fumble recovery, becoming the first player since 1999 to score on two defensive returns in the same game.
With Tennessee, he had career highs of six interceptions in 2004 and 64 tackles in 2003.