Wilcox agreed to a one-year deal with the Falcons on Monday, Will McFadden of the team's official site reports.
Wilcox suited up for seven games between the Colts and Jets last season without a single start, notching seven tackles in that span. The 28-year-old projects to provide the Falcons with depth at the safety position behind Keanu Neal (knee) and Ricardo Allen (Achilles).