Weekes, 32, was 4-6-2 with a 3.39 goals-against average in 14 games for the New York Rangers last season.
He's likely to see even less action in 2007-08, as Brodeur appeared in 78 contests last season, going 48-23-7 with a 2.18 GAA.
"Kevin Weekes has played more than 300 career NHL games and will bring added experience as a backup goaltender to Martin Brodeur," said Devils GM Lou Lamoriello.
Weekes has appeared in 323 regular-season games over eight full NHL seasons with Florida, Vancouver, the New York Islanders, Tampa Bay, Carolina, and the Rangers. The Toronto native recorded a career-high 23 victories and six shutouts with Carolina in 2003-04.